Into a mixing bowl, sift together the flour, baking powder, baking soda and salt. Cut the butter and shortening in the dry ingredients until it resembles wet sand. Stir in the buttermilk just until the dough comes together. Turn dough onto a well-floured surface, dust top with flour and gently knead 4 or 5 times. Press into a ½ inch thick square about 8x10 inches. Cut the dough into 6 4-inch squares and transfer to a baking sheet. Bake until golden brown, about 15 to 20 minutes. Remove from the oven and allow to cool.
Season the eggs with salt and pepper. In a large nonstick skillet, over medium heat, melt the butter. Add the eggs and gently stir until the eggs start to set. Swirl the pan so that the egg evenly coats the bottom in a thick sheet. Lower the heat, cover the pan and cook until the eggs are cooked. Turn out of the pan onto a plate and allow to cool. Cut into 6 even slices.
In the pan, brown the sausages on both sides.
Split each biscuit in half horizontally. Place a sausage on each bottom half, top with a slice of the omelet and top with an ounce of cheese. Replace the top of the biscuit. Place each sandwich on a baking sheet and bake until the cheese is melted, about 5 minutes. Serve warm.