Preheat oven to 350 degrees.
Remove disk of dough 10 minutes before you're ready to work with it. Using a rolling pin, roll dough crust out on a well floured surface. Be sure to roll from the center, and turn the dough 1/8 turn every few rolls. You can use a piece of parchment paper to ensure the dough doesn't stick to your countertop if needed! Roll dough out to about 1/8 inch thickness.
Using a round pastry cutter or glass which is just larger than your mini tart pans, cut out pieces of dough and transfer to tart pan. If you're using a large tart pan, place the whole piece of rolled out dough in to your pan. Press dough up the sides, removing any excess dough that spills over the edge with a knife.
Prick the base of the dough with a fork a few times, and fit each tart pan with parchment paper. Top with baking weights, dry beans, or rice. This weighs the dough down, allowing it to bake without the filling in it first, so it doesn't underbake. Bake for 12 minutes, removing from the over to slightly cool.
As the dough bakes, prep the apples. Using a mandoline or a very sharp knife, carefully cut very thin slices of the apple (mine were 1/16 inch), placing them in a bowl of warm water. This helps them be pliable so you can bend them in to the tart pan.
Once dough has cooled, add frangipane to slightly cooled tart shells, filling each almost to the top. Of course, if you're using a larger tart pan, add all the frangipane to the pan. Smooth out the top with a spatula.
Transfer apple slices from water to a paper towel so they aren't wet when you place them on the frangipane. Starting from the outside, start add slices of apple to the perimeter of the tart. You can arrange them so they overlap , continuing to angle them more the closer to the center you get. Using a very thinly sliced pices of apple, roll it in to a circle, and place directly in the center of the tart. Complete with remaining tarts.
Bake completed tarts for 13-15 minutes, until frangipane is set and apples are soft. Serve plain or with whipped cream.