Take the dough out of the refrigerator, set it on a lightly oiled work surface, and divide into 4 equal pieces of about 7 ounces each. Roll each piece into a tight ball. Line a baking sheet with parchment and lightly oil it with olive oil or cooking spray. Set each ball at least an inch apart on the parchment. Lightly spray or brush the balls with olive oil and cover loosely with plastic wrap. Let the dough warm up and relax at room temperature for 1-1/2 to 2 hours.

If you have a baking stone, put it on the middle rack of the oven. If not, set a rimmed baking sheet upside down on the middle rack to serve as a baking platform. Heat the oven (regular or convection) to its highest setting. Fill a small bowl with bread flour or semolina, and dust a 12-inch-square area of a clean work surface with a generous amount. Prepare a peel for transferring the pizzas to the oven by dusting the peel with bread flour or semolina. (If you don't have a peel, use a rimless cookie sheet or the back of a rimmed baking sheet, also dusted with flour.)

Shape the dough: With floured hands, transfer one of the dough balls to the floured work surface. Sprinkle the dough lightly with flour and gently press it with your fingertips into a round disk--you're trying to merely spread the dough, not squeeze all the gas from it. With floured hands, carefully lift the disk of dough and rest it on the back of your hands and knuckles. Using the tips of your thumbs, stretch the outer edge as you slowly rotate the dough until it is 10 to 12 inches in diameter. The edge should be the only place where you exert any pressure. If necessary, let the dough hang off one of your hands so that gravity provides some of the stretch. Despite the pressure on the edge, it will remain thicker than the inner section of the dough, which should be nearly paper thin. Don't pull the dough forcefully into a circular shape or it will stretch from the center and possibly rip. If the dough begins to resist and keeps shrinking back into a smaller circle, lay it on the floured work surface and let it rest for about 2 minutes. While it is resting you can begin to stretch and shape another dough ball. Return later to the first dough and finish shaping it.

Top the pizza: In a small bowl, stir together the cheeses, olive oil, oregano, and thyme. Season to taste with salt and pepper.

Lay the shaped pizza dough on the floured peel and spread one-quarter of the cheese mixture evenly over the dough, leaving 1/2 inch of the outer rim topping-free.

Bake the pizza: Carefully slide the pizza onto the baking stone using a jerking motion to get it to slide. If it sticks to the peel, carefully lift the stuck section and toss a little flour under it. Bake until the edge is puffy and brown with a slight char and the underside is brown and fairly crisp, 5 to 7 minutes (the hotter the oven, the faster and better it will cook). Rotate it after 3 minutes for even browning. Remove the pizza from the oven with either the peel or a long metal spatula and put it on a cutting board. While the first pizza is cooking, shape and top the remaining pizzas.

Leftovers: If you decide not to make all the pizzas, bake any remaining shaped dough as untopped pizza, brushed with olive or garlic oil prior to baking, and serve or save as flatbread.

Combine the flour, sugar or honey, salt, yeast, and olive oil in a large mixing bowl or in the bowl of an electric stand mixer. Add 11 fluid ounces (1-1/4 cups plus 2 tablespoons) cool (60 degrees to 65 degrees F) water. With a large spoon or the paddle attachment of the electric mixer on low speed, mix until the dough comes together in a coarse ball, 2 to 3 minutes by hand or 1 to 2 minutes in the mixer. Let the dough rest, uncovered, for 5 minutes.

Knead the dough: If using an electric mixer, switch to the dough hook. Knead the dough for 2 to 3 minutes, either by hand on a lightly floured work surface or with the mixer's dough hook on medium-low speed. As you knead, add more flour or water as needed to produce a ball of dough that is smooth, supple, and fairly tacky but not sticky. When poked with a clean finger, the dough should peel off like a Post-it note, leaving only a slight residue. It may stick slightly to the bottom of the mixing bowl but not to the sides.

Chill the dough: Lightly oil a bowl that's twice the size of the dough. Roll the dough in the bowl to coat it with the oil, cover the top of the bowl tightly with plastic wrap, and refrigerate for at least 8 hours and up to 3 days. It will rise slowly in the refrigerator but will stop growing once completely chilled. If the plastic bulges, release the carbon dioxide buildup by lifting one edge of the plastic wrap (like burping it) and then reseal. Use the dough for pizzas, calzones, or stromboli as directed in the recipes.

Make Ahead: It's best to mix the dough at least a day before you plan to bake. The dough keeps for up to 3 days in the refrigerator or for 3 months in the freezer. To freeze the dough: After kneading the dough, divide it into 4 pieces for pizzas or calzones or 2 pieces for stromboli. Freeze each ball in its own zip-top freezer bag. They'll ferment somewhat in the freezer, and this counts as the rise. Before using, thaw completely in their bags overnight in the fridge or at room temperature for 2 to 3 hours. Then treat the dough exactly as you would regular overnighted dough, continuing with the directions for making pizzas, calzones, or stromboli.

Variations: Whole Wheat Pizza Dough: Replace 25% to 50% of the flour with an equal amount of whole wheat flour. It may be necessary to add more all-purpose flour as you knead. Your goal is to produce a ball of dough that is smooth, supple, and fairly tacky but not sticky. It may stick slightly to the bottom of the mixing bowl but not to sides of the bowl. When poked with a clean finger, the dough should peel off like a post-it note leaving only a slight residue.

Cornmeal Pizza Dough: Replace 25% to 50% of the flour with an equal amount of cornmeal. Start with the same water as in regular dough and adjust from there, adding more flour until the dough, when poked with a clean finger, peels off like a post-it note, leaving only a slight residue. You may need to add up to 10 tablespoons of flour to get the right consistency: supple and tacky (almost but not quite sticky).The amount of extra flour will depend on the type of cornmeal. Polenta, for instance, absorbs much more slowly than fine grind cornmeal. Because cornmeal often takes a little longer to fully hydrate, you'll find that the dough will firm up slightly as it cools in the fridge.