01 - In a small bowl, whisk eggs with milk or cream, salt, black pepper, and smoked paprika until fully combined.
02 - Preheat a nonstick skillet over medium heat. Add butter, followed by red bell pepper and green onion. Cook, stirring, until softened, about 2 minutes.
03 - Pour the egg mixture into the skillet with the vegetables. Scramble gently until the eggs are softly set, 2 to 3 minutes. Transfer to a plate and set aside.
04 - Lay one flour tortilla on a clean cutting board. Sprinkle half of the cheddar and Monterey Jack cheese on the surface. Top evenly with scrambled eggs, shredded chicken, and sautéed vegetables. Distribute the remaining cheese over the fillings and cap with the second tortilla.
05 - Heat a large skillet or griddle over medium. Carefully transfer the assembled quesadilla to the hot pan. Cook for 2 to 3 minutes per side, pressing lightly with a spatula, until both sides are golden brown and the cheese is completely melted.
06 - Remove the quesadilla from the skillet and let rest for 1 to 2 minutes. Transfer to a cutting board, slice into wedges, and serve immediately.