Combine 4 cups flour, baking powder, and salt in a large bowl. Cut in shortening with a fork until coarse crumbs form.
Whisk egg yolks, cold water, and lemon juice together in another bowl. Stir into flour mixture with a fork until dough comes together into a ball; divide in half. Roll out 1 half and press into the bottom of a 10x15-inch baking pan.
Combine apples, sugar, 1/4 cup flour, and ground cinnamon in a bowl to make filling. Spread over dough in the pan.
Roll out remaining dough and lay on top of filling. Brush with milk. Cut slits in the dough with a sharp knife.
Bake in the preheated oven until golden brown, 45 to 50 minutes. Cool before cutting into 24 bars, at least 20 minutes.