In a saucepan, cook the ground sausage over medium heat, breaking up the meat with a wooden spoon, until cooked through. Drain the fat, and chill the sausage well. I recommend cooking the sausage a day in advance, so it can chill in the refrigerator and be ready to go when you make your biscuits.
In a bowl, combine the flour, corn starch, baking powder and salt. Use a pastry cutter to cut in the butter until crumbly.
Stir in the cooked and chilled sausage, the cheese and the diced peppers.
Stir in 3/4 cup of the milk, just until moistened and you have a shaggy dough. There will be some moist, sticky bits, and some dry bits, and that's exactly how it should be. If it seems too dry, add a little more milk, a tablespoon at a time. You don't want the dough too wet, though; it should be just moist enough to barely hold together.
On a lightly floured surface, gently roll the dough out to 1 inch thick, using a little more flour as needed to keep the dough from sticking.
Fold the dough into thirds, then thirds again, then roll the dough out again to 1 1/2 inches thick.
Cut into rounds with a 2 1/2 or 3 inch biscuit cutter, trying to cut as many biscuits as you can the first time. Do not twist the cutter, just cut straight down and lift it straight back up. Gather up the scraps, press them together and cut those as well. You should be able to cut around 12-15 biscuits.If you like, you can also use a sharp knife or a bench scraper to cut square biscuits, which will reduce the amount of dough scraps that you need to re-roll. Line a baking sheet with parchment paper, and place the biscuits close together, nearly touching. Freeze the cut biscuits for 30 minutes.
While the biscuits are freezing, preheat the oven to 450 F and position a rack in the center of the oven.
Use a pastry brush to lightly brush the beaten egg over the tops of the chilled biscuits.
Bake the biscuits until risen, fluffy and golden brown on top, about 15-17 minutes.
Cool biscuits for 5 minutes, then serve hot with softened butter. Sprinkle the tops of the biscuits with flaky salt and ground black pepper.