Sift together the flour, salt, and baking powder. Cut in shortening and butter until mixture is like coarse meal. Stir in cheese, beaten egg, and milk, stirring just until all ingredients are moistened. Roll 1/2-inch thick on a lightly floured surface; cut into squares or rounds. Bake at 400° for 20 minutes. Split and serve with Egg Sauce.
While Biscuits are cooking, make egg sauce. In a saucepan, melt 3 tablespoons butter; stir in flour until smooth and bubbly. Gradually stir in milk. Continue to cook, stirring constantly, until thickened. Stir in salt, red pepper, parsley and eggs.