Prepare the sweet tart shell. Prepare the Sweet Tart dough according to the instructions. Line the tart pan with the dough, place the weights inside, and bake for 30 minutes. Remove from the oven; take out the pie weights and the liner. Wrap a large piece of aluminum foil a round the outside of the tart pan so that it comes up the outer sides of the pan and drapes over the browned edge of the shell. Pinch the foil around the edge so that it is covered (this will prevent the rim of the tart from over-browning). Return the tart to the oven and bake until the center of the shell has browned, about 15 to 20 minutes. Remove from the oven and allow it to cool, leaving the outer aluminum foil cover in place.
Make the brown butter and almond custard (see the Note on browning butter):
In a small frying pan, brown the butter over medium-high heat until it carmelizes and emits a nutty aroma. Remove from heat.
In the bowl of a stand mixer fitted with the paddle attachment, place the almond paste, sugar, and eggs and beat on medium-high speed until the mixture is thoroughly combined. Turn down to a slow speed and add the flour and salt to the almond mixture. Turn the mixture back up to medium speed and slowly drizzle in the brown butter. (The butter will emulsify into the almond cream, leaving the mixture smooth, creamy, and shiny.) once all the butter has been incorporated, add the crème fraîche and continue mixing on slow speed until thoroughly combined. Scrape down the sides of the bowl and set the custard aside.
Assemble and bake the tart:
Preheat the oven to 350°F. Position the rack in the center of the oven. Cover the bottom of the prebaked tart shell with the chopped almonds and pour the custard on top. Press the sliced apricots into the custard. Bake until the custard puffs a bit and browns, 30 to 40 minutes. Allow the tart to cool for ½ hour on a wire rack before removing it from the metal tart ring.
Serve this tart slightly warm or at room temperature. This tart needs no accompaniment. It is crispy, creamy, tart, and sweet.
Plum and Almond Tart: This tart also works beautifully with fresh plums. Substitute the same amount of plums for apricots.