Preheat oven to 350° F. Lightly coat two large baking sheets with cooking spray. Set aside. Sift flour, baking powder, salt, and sugar into a large mixing bowl. Cut in butter and vegetable shortening with a pastry blender or two knives until dough resembles coarse meal. Mix in egg yolks.

Beat egg whites: In a medium bowl, beat egg whites and almond extract with mixer until soft peaks form — about 3 minutes. Fold whites into dough. Mix in orange juice.

Turn out dough onto a lightly floured surface and knead briefly until dough comes together and is smooth — about 2 minutes. Roll out dough into a 9- by 12-inch rectangle about 1/2 inch thick. Using a fluted pastry cutter or a sharp knife, cut down the 12-inch length of the rectangle to divide the dough into four 3-inch-wide strips. Cut each strip into four 3-inch squares. Cut along the diagonal of each square to form 24 triangles.

Place cookies on baking sheet and sprinkle almonds over each cookie. Press almonds lightly into dough. Bake until edges are lightly browned — 7 to 10 minutes. Remove from baking sheet and cool on a wire rack. Store in an airtight container.