01 - In a mixing bowl, whisk together eggs, milk or cream, salt, black pepper, and smoked paprika until thoroughly mixed.
02 - Heat butter in a nonstick skillet over medium heat. Add red bell pepper and green onion. Cook, stirring occasionally, until softened, about 2 minutes.
03 - Pour the egg mixture into the skillet with vegetables. Cook, gently scrambling, until eggs are softly set, about 2-3 minutes. Remove from heat and set aside.
04 - Lay one tortilla on a work surface. Sprinkle half of the cheddar and Monterey Jack cheese evenly over the tortilla. Top with scrambled eggs, cooked chicken, and sautéed vegetables. Add remaining cheese, then place the second tortilla on top.
05 - Heat a large skillet or griddle over medium heat. Carefully transfer the assembled quesadilla to the skillet. Cook for 2-3 minutes per side, pressing lightly with a spatula, until both sides are golden brown and crisp and the cheese is fully melted.
06 - Remove the quesadilla from the skillet. Let it rest for 1-2 minutes, then cut into wedges. Serve immediately.