Shape the dough into a 9x13-inch rectangle that will fit into a well-buttered 9x13-inch baking pan. Press the dough into the pan (don't worry about any folds--they'll add to the cake's character). Cover the pan and proof the dough until it looks puffy but hasn't doubled in volume, about 1-1/2 hours.

Cut the chilled butter into tiny chunks and scatter them evenly on the dough surface. Push the butter chunks down to the bottom of the dough with your fingertip, taking care not to poke all the way through to the pan. Spread the dough with the sour cream and then sprinkle it with the sugar and sliced almonds.

Position an oven rack on the top spot and then heat the oven to 400 degrees F. Cover and proof the shaped dough until it's large, puffy, and remains indented when lightly pressed with your fingertip, about 1/2 hour. Bake until golden brown, 15 to 20 minutes, rotating the pan halfway through baking. Let cool on a rack.

In a large bowl, mix the 3 Tbs. flour with the yeast and then whisk in the water. Let the mixture sit covered until it has begun to puff, 10 to 15 minutes.

Fit a large-capacity food processor with the metal blade. Put the remaining flour in the workbowl and then add the yeast mixture, potato, egg yolks, vanilla, and sour cream. Process the dough for about 1 min. Remove it from the machine and knead it by hand on an unfloured countertop for 1 minute to redistribute the heat. The dough will be very stiff at this point. Continue this alternating kneading: process for 30 seconds and then knead on the counter for about 30 seconds, until the dough is very smooth (this should take 2 to 3 processing rounds).

Put the dough back in the food processor and add the sugar and salt, kneading again in the processor and then on the counter until the sugar has dissolved (the dough will soften considerably and become very sticky; this is fine).

Finally, return the dough to the processor, add the butter, and do another alternating kneading round until the butter is well incorporated and the dough is very soft and smooth, about 1 minute. The dough won't clean the bowl at this point. It's all right if it feels quite soft and warm after processing: kneading the dough on the counter will help it cool down and firm up.

Transfer the dough to a container at least four times its volume (no need to grease the container); seal well. (At this point, the dough can instead be rolled in flour and then sealed in a plastic bag and refrigerated for up to 4 days. If you do mix ahead and chill the dough, pull it out of the fridge 3 to 4 hours before baking.) Let the dough ferment at room temperature for about 3 hours or until it's expanded to 3 times its volume and an indent remains when you press it with a floured finger.