In a small bowl, stir together the egg yolk, water and vanilla; set aside.
To make the dough by hand, in a large bowl, stir together the flour, sugar and salt. Using a pastry cutter or 2 knives, cut the butter into the flour mixture until the texture resembles coarse cornmeal, with butter pieces no larger than small peas. Add the egg mixture and mix with a fork just until the dough pulls together.
To make the dough in a stand mixer fitted with the paddle attachment, stir together the flour, sugar and salt in the mixer bowl. Add the butter and beat on medium-low speed until the texture resembles coarse cornmeal, with butter pieces no larger than small peas. Add the egg mixture and beat just until the dough pulls together.
Transfer the dough to a work surface, pat into a ball and flatten into a disk. Use the dough immediately, or wrap in plastic wrap and refrigerate until well chilled, about 30 minutes.
To roll out the dough, on a lightly floured board, flatten the disk with 6 to 8 gentle taps of the rolling pin. Lift the dough and give it a quarter turn. Lightly dust the top of the dough or the rolling pin with flour as needed, then roll out until the dough is about 1/8 inch thick. Use a small, sharp knife to cut out a round or rounds 2 inches greater in diameter than your tart or larger tartlet pans. Use a small, sharp knife or a cookie cutter to cut out rounds 1/2 to 1 inch greater in diameter than your miniature tartlet pans. If using a rectangular tart pan, cut out a rectangle 2 inches larger on all sides than the pan. Makes enough dough for one 9 1/2-inch tart, six 4-inch tartlets, twelve 2-inch miniature tartlets or one 13 3/4-by-4 1/4-inch rectangular tart.