Preheat the oven to 450 degrees F (235 degrees C). Line a baking sheet with parchment.
Stir flour and cream together to form a dough. Use plastic wrap to shape into a round ½-inch thick patty. Transfer to a lined baking sheet.
Bake in the preheated oven until lightly golden brown, 12 to 15 minutes. Flip biscuit so the flat, darker side is up, and press lightly down so that it sits flat. Transfer to a cooling rack until needed.
Meanwhile, for sausage gravy, add butter and sausage to a small skillet over medium-high heat. Cook and stir sausage until browned, breaking into small crumbles with a spatula. Add green onions and cook, stirring, for 1 minute.
Add flour and cook, stirring, for 1 minute. Reduce heat to medium if needed and whisk in milk; add black pepper, cayenne, and salt. Wait for the gravy to simmer and thicken, stirring occasionally. Transfer egg into center of the skillet on top of gravy; cover and cook until the egg is cooked to your liking, 1 to 2 minutes.
To serve, spoon gravy over the biscuit and top with the egg. Spoon remaining gravy around the egg and biscuit, and top with sliced green onion.
