To make the crust, combine the flour, sugar, salt, and butter in food processor, electric mixer, or large mixing bowl. Using the blade attachment of the food processor, the paddle attachment of the electric mixer, or a pastry cutter, cut the cold butter into the flour until the mixture resembles a coarse meal. If you are using a processor, transfer the mixture to a bowl. Sprinkle the 2 tablespoons water and the vanilla over the mixture and mix with a fork until the dough clumps together. Gather the dough into a ball, wrap it in plastic wrap, and flatten into a 1-inch-thick disk. Refrigerate the dough for 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 the dough into a 13-inch circle. Set the rolling pin on top of the dough on the diagonal, and flip the dough edge (about one-third of the dough width) over the rolling pin. Holding the 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 the dough to leave about a 1/2-inch overhang all the way around, saving the trimmings at room temperature for later crust repair work. Gently push the dough into the pan so that it fits snugly against the sides, then fold the overhang toward the inside, pressing the folded dough against the sides. With thumb and forefinger, gently pinch the dough so that the sides of the tart extend about 1/4 inch above the edge of the pan, with an even thickness all the way up and around. Freeze the crust for 30 to 40 minutes, until it is hard. While the crust is chilling, preheat the oven to 350 degrees. When the 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 the crust for 35 minutes, then remove the weights and foil and bake for another 15 minutes, until the crust is golden brown and feels dry. If holes developed anywhere in the crust, they can easily be patched now by gently spackling with the leftover dough, but be careful not to break the tart sides while making repairs. Whisk the egg with 1 teaspoon of water to make an egg wash and brush all over the bottom and sides of the crust. Return the crust to the oven and bake for 5 minutes more, until the egg is set and dry. Set the crust aside on a rack to cool. About 15 minutes before the crust will finish baking, make the filling: Whisk the eggs and granulated sugar together in a bowl until smooth. Whisk in the lime juice and lemon juice, until smooth. Whisk in the cream, then strain the filling through a fine-mesh sieve into a large measuring cup and stir in the lemon zest. The filling will be quite liquid at this point. Without removing the crust from the oven, pour the filling into the crust (it's easier to do it this way than to juggle the full pie shell from counter to oven). Reduce the oven heat to 325 degrees and bake the pie for 35 to 40 minutes, until the center is just set. Cool the pie on a rack, then refrigerate until cold. To prepare the meringue, place the egg whites and cream of tartar in an electric mixer fitted with the whip attachment. Place the brown sugar in a small, heavy saucepan, add water to cover, attach a candy thermometer to the pan, and turn the heat on high. When the sugar is at about 240 degrees, start whipping the whites on high speed (they should be foamy and starting to thicken before you add the sugar). When the sugar is at the high soft-ball stage (245 degrees), remove the thermometer from the sugar and, with the mixer still running, carefully avoiding the whip, pour the sugar into the egg whites in a thin stream. When steam starts to come off the whites, add the sugar more quickly. When all sugar has been added, continue whipping until firm but soft peaks form. The meringue should still be quite warm. Quickly spread the meringue on top of the pie, shaping it with a rubber spatula to form a high, smooth dome. With the back of a soup spoon, make decorative waves, working quickly because as the meringue cools it will become stiff and difficult to shape. Preheat the broiler and place the pie on a lower oven rack to brown, turning every few seconds to brown evenly. Store the finished pie in the refrigerator, but plan on serving it within 3 to 5 hours, as the meringue may start to weep.