for the crust
2 1/2 cups all purpose flour
1 tablespoon sugar
3/4 teaspoon salt
10 tablespoons (1 1/4 sticks) chilled unsalted butter, cut into 1/2-inch pieces
1/3 cup chilled solid vegetable shortening, diced
6 tablespoons (or more) ice water
for the filling
10 apples, very thinly sliced (I used pink lady apples, but red delicious are fine too) Do not peel.
3 tablespoons lemon juice
1/2 cup sugar (more if your apples are super tart)
4 tablespoons corn starch
1/4 cup apricot jam, mixed with 1 tablespoon lemon juice
You will also need: a 12-cup muffin pan
Blend flour, sugar and salt in processor. Add butter and shortening and cut in using on/off turns until mixture resembles coarse meal. Add 6 tablespoons ice water and process until moist clumps form, adding more water by teaspoonfuls if dough is dry. Gather into ball, then flatten into a disk. Wrap in plastic and chill 2 hours.
In a steamer basket, over a bit of boiling water, steam the apple slices for 4-8 minutes, depending on thickness. Because you will be putting the apple slices into a small space and they do not bend well, you need to soften them a little bit to be pliable, but you do not want them to become mushy. Keep checking a slice to see if you can bend it without the slice breaking, but they are still sturdy. Once they are at that stage, remove from the steamer basket and gently combine with the lemon juice, sugar and corn starch in a medium bowl, and toss gently to coat.
Preheat oven to 400F. Spray your muffin pan with cooking spray. Roll out dough to 1/3 inch thickness. Using a round biscuit cutter, cut out rounds and nestle them into the muffin pan. Crimp edge and dock bottom. Carefully arrange apple spices in a circle. This is time consuming, but makes a pretty presentation.
Bake in oven for 30-40 minutes, or until crust is browned and the apples are soft. Remove from oven and allow to sit for 20 minutes or so before serving. While tarts are cooling, combine apricot jam and lemon juice in a small bowl and microwave for 15 seconds. Brush with a pastry brush to give the tart a nice sheen.