Slice the apricots 3/4-inch thick, discarding the pits. Place the apricots in the prebaked tart shell in a decorative pattern. Set aside.
Combine the sugar, egg yolks, and cream in a medium mixing bowl. Whisk until combined. Stir in the flour and salt. Carefully pour the creamy mixture over the apricots.
Sprinkle the almonds over the top of the tart. Bake until the custard is almost completely set, about 35 to 40 minutes. Serve slightly warm or at room temperature.
In a small bowl, mix the egg and cream together. Set aside.
In the bowl of an electric mixer, combine the flour, sugar, salt, and butter. Using the paddle attachment on low speed, mix in the butter until it is the size of small peas. With the mixer on low speed, add the egg mixture. Mix the dough just until it is no longer dry looking. It will still be loose and crumbly at this point.
Place the dough on the work surface. With your hands, combine and form the dough into a single ball. Wrap the dough in plastic wrap and refrigerate until firm but still malleable.
Roll out dough and fit it into a 9 1/2-inch tart shell. Prebake the shell in a preheated 325 degree F oven until golden brown, about 15 minutes