Preheat oven to 400 degree F. Lightly grease baking sheets; set aside. In a large bowl stir together flour, baking powder, red pepper (if using), and salt. Using a pastry blender, cut in shortening until the size of coarse crumbs. Stir in 1/2 cup finely shredded cheese. Add the 3/4 cup milk, stirring just until dry ingredients are moistened. Form into a ball.
On a lightly floured surface, roll dough to a 10-inch square, 1/4 inch thick. Brush with the 1 tablespoon milk and sprinkle with 1/2 cup finely shredded cheese; press lightly. Cut into sixteen 2-1/2-inch squares. Cut each square in half diagonally to make 32 triangles. Place on the prepared baking sheets.
Bake about 12 to 15 minutes or until golden brown. Serve warm. Makes 32 triangles.