01 - In a small bowl, whisk eggs with milk or cream, salt, black pepper, and smoked paprika until smooth and well combined.
02 - Heat a nonstick skillet over medium heat and add butter. Add red bell pepper and green onion and cook, stirring frequently, until vegetables are softened, about 2 minutes.
03 - Pour the egg mixture into the skillet with vegetables. Gently scramble until eggs are softly set, approximately 2 to 3 minutes. Remove skillet from heat and set mixture aside.
04 - Place one tortilla on a clean surface. Sprinkle half of the cheddar and Monterey Jack cheeses evenly over the surface. Layer with the scrambled eggs, chicken, and sautéed vegetables. Top with the remaining cheese.
05 - Place the second tortilla on top to form the quesadilla.
06 - Heat a large skillet or griddle over medium heat. Carefully transfer the assembled quesadilla to the skillet. Cook for 2 to 3 minutes per side, pressing gently with a spatula, until tortillas are golden brown, crisp, and the cheese is melted.
07 - Remove from heat, let rest for 1 to 2 minutes. Slice into wedges and serve immediately.