To make the dough: In a small bowl, whisk together the egg yolk, water and vanilla; set aside.
Put the flour, sugar and salt in the bowl of a food processor fitted with the metal blade and pulse until combined. Add the butter cubes and pulse until the mixture resembles oatmeal with some larger (roughly pea-sized) clumps. Drizzle the yolk mixture over the flour mixture and pulse just until the dough forms a ball.
Transfer the dough to a lightly floured 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. (The tart dough may be made ahead and frozen for up to 1 month.)
Remove the dough from the refrigerator. Place it between 2 sheets of parchment paper and roll it into a 13-inch round. Slide the dough, still between the parchment, onto a baking sheet, and refrigerate for 20 minutes.
Preheat the oven to 375 F.
Remove the baking sheet and dough from the refrigerator. Remove the top sheet of parchment. Pile the fruit in the center of the dough, leaving a 2-inch border of dough. Sprinkle the fruit with 3 teaspoons of the sugar and dot with slivers of butter. Fold the edges of the dough over the fruit to partially cover it. Chill until firm, about 10 minutes.
Whisk together the yolks and cream to make an egg wash. With a pastry brush, paint the egg wash onto the edges of the dough. Sprinkle with the remaining 2 teaspoons sugar.
Bake the tart for 45 to 50 minutes, or until the pastry is dark brown. Remove to a wire rack and serve warm or at room temperature.