Heat the oven to 375°F and grease a 9×13-inch baking dish. Line a sheet pan with parchment for par-baking the biscuit pieces.
Cut each biscuit into 6 small pieces. Spread the pieces on the lined sheet pan and par-bake for 8 minutes, just until puffed and lightly set (not browned). Transfer the pieces into the greased baking dish in an even layer.
Cook the sausage: Warm a large skillet over medium-high heat. Add the sausage and crushed red pepper and cook, breaking it into crumbles, until browned and cooked through, 6–8 minutes. Using a slotted spoon, move the sausage to a plate; leave about 2–3 tablespoons of drippings in the pan.
Make the gravy: Reduce heat to medium. Add the butter to the skillet (add enough to yield roughly 3 tablespoons total fat). Sprinkle in the flour and whisk for 1 minute. Slowly stream in 2 1/4 cups milk while whisking. Season with salt, black pepper, and garlic powder. Simmer, whisking often, until the gravy is creamy but still pourable, 3–5 minutes. Stir in about one-third of the cooked sausage and remove from heat.
Whisk the eggs in a bowl with 1/4 cup milk and a small pinch of salt. Stir in 1/2 cup of the cheddar. For extra flavor, whisk in 2 tablespoons of the warm gravy to temper, then return it to the bowl (optional).
Assemble: Scatter the remaining sausage over the par-baked biscuit layer. Drizzle about half of the gravy evenly over the top. Pour the egg mixture across the dish, then sprinkle with the remaining cheddar. Spoon the rest of the gravy in several broad swirls over the surface so it bakes into creamy pockets.
Bake on the center rack at 375°F for 25–30 minutes, until the eggs are set in the center and the edges are deeply golden. For a bubblier top, broil for 1 minute at the end, watching closely.
Rest for 10 minutes so the gravy settles, then finish with chives and extra black pepper to taste. Slice and serve warm.