Method for pastry crust:Preheat oven to 450° F (230° C).
In the food processor: Blend the butter into the flour. Add the sugar and lemon zest and process until the mixture looks sandy. Add the yolk and 1 tablespoon of water. If the dough is flexible and holds together well, add no more water. If it’s not coming together, add water by teaspoons, processing after each addition and stopping when a ball of dough forms.
By hand:Sift the flour into a large bowl. Rub the butter into it until sandy. Add sugar and mix well. Add beaten yolk, lemon zest and 1 tablespoon of water. Add more water by teaspoons to make a flexible dough. Knead lightly for a few minutes.
Roll the dough out lightly on a floured surface. Place it in a greased tart or pie pan. If your kitchen is very warm, put it in the fridge for the few minutes it takes to prepare the filling.
Method for apricot filling:Halve the apricots and remove the pits. Set them to macerate in the sugar and vanilla while preparing the crust.
Cook the apricots, with any juices, covered, over low heat for 5 minutes.
Remove the apricots from the liquid. Keep the liquid in the pan.
Arrange the apricot halves in a circle on the pastry. Dust the edges with sugar.
Bake for 10 minutes.
Lower the heat to 375° F (190° C) and bake 30-40 minutes longer, until the crust is baked.
While the tart is in the oven, reduce the liquid from the cooked apricots to a syrup by boiling it down. If there are only a few tablespoons to begin with, augment it by adding 2 tablespoons of sugar and 2 tablespoons of water and cooking it all down together.
When the tart is baked, remove it from the oven and pour the syrup over it.