01 - In a mixing bowl, thoroughly whisk together the eggs, milk or cream, salt, black pepper, and smoked paprika until evenly blended.
02 - Heat the nonstick skillet over medium heat. Add unsalted butter, then sauté red bell pepper and green onion until softened, about 2 minutes.
03 - Pour the egg mixture into the skillet with the vegetables and gently scramble on medium heat until softly set, about 2 to 3 minutes. Remove from heat and set aside.
04 - Place one tortilla on a clean cutting board. Evenly sprinkle half of both cheeses over the tortilla, then layer with scrambled eggs, chicken, and the sautéed vegetables. Top with the remaining cheese and the second tortilla.
05 - Preheat a large skillet or griddle over medium heat. Carefully transfer the assembled quesadilla to the skillet and cook for 2 to 3 minutes per side, pressing lightly with a spatula until golden brown and the cheese has fully melted.
06 - Remove the quesadilla from heat and allow it to rest for 1 to 2 minutes. Slice into wedges and serve immediately.