Put the flour, sugar, and salt in a food processor. Pulse 3 to 4 times to blend. Distribute the butter in the bowl and pulse 7 to 8 times. Process until the mixture resembles coarse meal, 8 to 10 seconds. In a small bowl, beat the egg, egg yolk, water, and vanilla with a fork. Pour the egg mixture over the flour mixture and pulse 5 to 6 times. Process until the mixture just begins to form a mass, 8 to 10 seconds. Empty the dough onto a lightly floured surface and knead 6 to 8 times until the dough is just smooth and malleable. Shape it into an evenly thick 6-inch square. Using a pastry scraper or the dull side of a long knife, score the dough at 1-inch intervals so you get thirty-six 1-inch squares. Cover the dough with plastic wrap and chill for at least 20 minutes.

Lightly spray the muffin tins with vegetable oil (not necessary for nonstick tins). Using the score lines as a guide, cut the dough into 36 1-inch pieces. Roll each piece into a ball in your palms (lightly flour your hands, if necessary). Put one ball in the center of each muffin cup.

If you have a wooden tart tamper, flour it lightly. Press the wider end onto a ball of dough until the dough thins out and begins coming up the sides of the cup, and then twist the tamper slightly to release it. Use the tamper's narrower end to push the dough halfway up the sides and to smooth out the dough where the sides meet the bottom. (If you don't have a tart tamper, use a narrow, flat-bottomed glass or your fingers, lightly floured, to press the dough into the cups.)

Tilt the muffin tin to see if the dough reaches the same level in all the cups; also check for any holes in the dough (this could cause the tartlet to stick to the pan). Rub your thumb around the rim of the dough in each cup for a clean, smooth edge. Slightly less than 1/2 inch of each cup should be exposed. Chill for at least 10 min. to firm the dough before filling and baking.

If you can't find superfine sugar, make your own by processing granulated sugar in a food processor for a few seconds.