In a bowl, combine your flour, salt, sugar, and vegetable shortening. With your fingers, start to work the shortening into the flour until it develops very fine and small crumbs. Add your cold sliced butter and work it in with your fingers. Stop when the butter is around the size of hazelnuts. This will help create flaky layers. Add enough cold water until all the flour is hydrated and the dough just comes together. Plastic wrap and place into the refrigerator to rest for 30-45 minutes.
Peel and halve the granny smith apples. Core and slice, then toss the apples in with the sugar, cinnamon, lemon juice, and salt.
Take out the pate brisee and scale out approximately 60g per tart. Roll it into a ball and place on lightly floured surface. Roll it out with a rolling pin until it is about 5" in diameter. Tightly arrange the apples in the center of the circle. Pull the excess dough on the edges over the top and press down slightly.
Wash with melted butter and finish with granulated sugar sprinkled on top before baking. Bake for 15 minutes or until golden brown.