To make the crust, put the flour in a large bowl. Add the sugar and mix. Using your hands, make a well in the center. Place the butter pieces and egg yolk in the well. Using your fingers, work the butter and egg yolk together until well combined then work the butter-egg mixture into the flour mixture until combined. The dough will be crumbly, but when you squeeze a handful in your hand, it should hold together.
Sprinkle into a 10-inch pie or tart pan. Press the dough firmly and evenly onto the bottom of the pan. Make ropes of the dough and press them onto the walls, making sure not to let the crust thicken at the corners. It should make a clean right angle where the sides meet the bottom. Chill the crust at least 30 minutes or, covered, up to 3 days.
Preheat the oven to 375 degrees F.
To make the frangipane filling, in a food processor fitted with a metal blade, pulse the almonds and sugar just until sandy. Do not over-process, or the mixture will become pasty. Add the butter and process just until blended. Add the eggs and process until blended. Scrape down the sides of the bowl, add the vanilla and flour, and process until smooth (you have just made a frangipane). Spoon the frangipane into the unbaked tart shell. Bake until the frangipane is golden brown and puffy and the crust is golden brown, 45 to 50 minutes.
Let cool. Spread 3/4 cup apricot preserves on the surface of the baked tart to act as a bed for the fruit. Slice fruit and arrange it decoratively. Heat the remaining 1/4 cup apricot preserves with the water until boiling and smooth. Brush the fruit with the apricot preserves to protect the fruit from drying out and make it glisten.