Prepare a tart pan by greasing it lightly.

Preheat your oven to 400 degrees F.

Make the dough in your food processor fitted with the metal blade. Process 1 cup of flour, 1/2 C. sliced almonds, 1/4 C. granulated sugar and the salt until the nuts are finely ground. Pulse the chilled butter pieces into the flour mixture and continue to process until the mixture looks like coarse meal. Now, add the egg yolk and process until the dough just begins to come together and form clumps.

Remove the dough from your processor and press it into the bottom of your tart pan with your fingers. Try to get the dough evenly distributed in the tart pan and be sure to push some of the dough up the sides of the pan so that your tart will have a pretty edge. Cover the tart pan with plastic wrap and let the dough chill in your refrigerator for at least an hour. The dough will feel fairly firm when you remove it from the refrigerator. Once removed from the refrigerator, use the tines of your fork to poke holes into the bottom of the tart shell. Make about a dozen holes. Bake the tart shell in your 400 degree F. oven for about 20 minutes. If the shell begins to puff up while baking, press the dough down with the back of a heat-proof spatula. When the tart shell is baked, remove it from the oven and let it cool while making the filling.

Decrease oven temperature to 375 degrees F.

Use the same food processor with the same metal blade for making the filling. There is no need to clean the bowl. Process together 1/2 C. flour, brown sugar, almond paste and 1/4 C. sliced almonds until you can see that the almond paste is broken into fine pieces in the flour mixture. Add 4 T. chilled butter and process the mixture until the butter pieces have begun to break down. The butter pieces should now be about the size of peas. Set aside but move quickly to put the tart together.

Prepare your fresh apricots by halving and pitting them and slicing them into 1/2-inch slices. Toss the sliced apricots into a bowl with the cornstarch and 1/4 C. sugar (or a bit more if your apricots aren't particularly sweet).

Spread the apricot slices (now softening in the sugar/cornstarch mixture) evenly in the bottom of the tart pan. You wil want to include as much of the cornstarch and sugar mixture that is now clinging to your apricots in your pie. The cornstarch will thicken the apricot juices so that your pie won't be runny. The sugar will diminish any excessive tartness in the apricots.

Sprinkle the almond/flour mixture over the apricots that you have now arranged in the tart shell. Using your hands, be sure the crumbly almond/flour mixture is distributed evenly on top of the apricots.

Bake until the fruit is bubbling and the topping is beginning to brown. This will take about 30 minutes. Watch your tart carefully at the end of baking. You don't want your crust to burn. Remove your tart from the oven and let it cool to allow the fruit juices to thicken and to make it easier to cut neat slices to serve your guests..

This tart is best served warm or at room temperature and would be spectacular with a scoop of good quality vanilla ice cream.