Preheat oven to 375, butter bottom and sides of tart pan. In large bowl, combine butter and sugar and stir to blend. Add almond and vanilla extracts, salt, and flour, and stir to form a soft, cookie-like dough. Do not let it form a ball. Transfer the dough to the center of the tart pan. Using the tips of your fingers, evenly press the pastry onto the bottom and sides of the pan. The dough will be quite thin. Place pan in center of oven and bake until dough is slightly puffy and set, about 12 to 15 minutes. Sprinkle the ground almonds on the crust to prevent it from getting soggy later.

Prepare the cream: in a medium bowl, combine cream, egg, almond and vanilla extracts, and honey; whisk to blend. Whisk in the flour. Starting just inside the edge of the pastry pan, neatly overlap the halved fruit, cut side up, at a slight angle. Make 2 or 3 concentric circles, working toward the center. Fill the center with the remaining apricots.

Pour the cream evenly over the fruit. Place in the center of the oven and bake until the filling is firm and the pastry is a deep golden brown, 50 to 60 minutes. The fruit will shrivel slightly. Remove to a rack to cool, and sprinkle with confectioner's sugar just before serving.