In a food processor (electric mixer or large mixing bowl) combine flour, sugar, salt, and butter. Using the blade attachment of food processor (or paddle attachment of electric mixer) cut cold butter into flour until mixture resembles coarse meal. If you are using a processor, transfer to a bowl.
Sprinkle 2 tablespoons water and the vanilla over the mixture and mix with a fork until dough clumps together. Gather dough into a bowl, wrap it in plastic wrap, and flatten into a 1-inch thick disk. Refrigerate dough 30 minutes, until it is firm enough to roll out.
Have ready an 11-inch fluted tart pan with a removable bottom (or a 9-inch deep-dish pie pan).
On a lightly floured surface, roll out dough into a 13-inch circle. Set rolling pin on top of dough on the diagonal, and flip dough edge (about one-third of the dough width) over rolling pin. Holding dough against the pin gently with one hand, pick up the pin and set the dough in the tart pan, centering it as well as you can.
Trim dough to leave about 1/2 inch overhang all the way around, saving the trimmings at room temperature for later crust repair work. Gently push dough into pan so it fits snugly against the side, then fold overhang toward the inside, pressing the folded dough against the side. With thumb and forefinger, gently pinch dough so that sides of the tart extend about 1/4 inch above edge of pan, with an even thickness all the way up and around. Freeze the crust for 30 to 40 minutes, until hard. Toward the end of freezing time, preheat the oven to 350 degrees.
When crust is hard, line it with a piece of aluminum foil large enough to cover it, and fill with beans, rice, or pie weights. (Do not prick the crust!) Bake crust in preheated oven for 35 minutes, then remove weights and foil and bake another 15 minutes, until crust is golden brown and feels dry.
Note: if holes developed anywhere in the crust, they can easily be patched now with leftover dough.
In a small bowl, whisk egg with 1 teaspoon water to make an egg wash and brush all over bottom and side of crust. Return crust to oven and bake 5 minutes more, until egg is set and dry.