Cook the sausage: Heat a nonstick skillet over medium. Add the sausage and cook, breaking it up with a spatula, until browned and cooked through, about 5–7 minutes.
Transfer to a plate and drain any excess grease if needed.
Beat the eggs: In a bowl, whisk the eggs with milk or water, a pinch of salt, and black pepper. Add paprika or chili powder if you like a mild kick.
Scramble gently: Wipe out the skillet if very greasy. Add 1 tablespoon butter or oil.
Pour in the eggs and cook over medium-low, stirring slowly until soft and just set. Remove from heat. Don’t overcook—they’ll finish inside the quesadilla.
Build the quesadilla: Place a tortilla on a cutting board. Sprinkle half the cheese evenly over the tortilla.
Top with half the eggs, half the sausage, and a bit of chopped onion if using. Finish with more cheese, then top with the second tortilla.
Crisp and melt: Return the skillet to medium heat and add the remaining butter or oil. Slide the assembled quesadilla into the skillet.
Cook for 2–3 minutes until golden brown underneath.
Flip carefully: Use a wide spatula to flip. Cook another 2–3 minutes until the second side is golden and the cheese is melted. Press gently with the spatula to help everything fuse.
Rest and slice: Transfer to a cutting board and let it rest 1 minute.
Slice into wedges. Serve with salsa, hot sauce, or a dollop of sour cream.