Heat the oven to 450°F (230°C). Whisk the flour, baking powder, soda, salt and sugar. Rub in the butter until pieces are pea-sized.
Stir in the buttermilk just until it comes together. Pat to 1 inch thick, fold in half, pat again, fold again, then cut 6 rounds without twisting the cutter.
Bake on a lined tray, touching, 14 to 16 minutes until tall and golden.
Meanwhile cook the sausage patties in a skillet over medium heat, 4 minutes a side. In the same pan fry the eggs until the whites set, covering with cheese for the last minute.
Split each warm biscuit, spread with the spicy mayo, add a patty and an egg with cheese, and close.
Tips
Cold butter and a light hand make the layers.
For a square baked egg like the bakeries, whisk 6 eggs with 1/4 cup milk, bake in a buttered 8-inch pan at 350°F for 15 minutes, and cut squares.