1. Preheat oven to 425 degrees Fahrenheit.
2. In a bowl, whisk together eggs and milk and season with salt and pepper.
3. In a skillet over medium heat, heat one tablespoon butter. Add the eggs and cook, stirring often, until light and fluffy. Transfer eggs to a bowl.
4. Heat the remaining tablespoon of butter. Add diced peppers and cook for five minutes, until soft.
5. Brush a rimmed baking sheet with one tablespoon oil. Place six tortillas around the edges of the pan so that about half of each tortilla hangs over the side. Place another tortilla in the center to cover the pan completely. Top with half the cheese, eggs, peppers, and then the rest of the shredded cheese.
6. Place the remaining tortilla in the center. Fold all the other tortillas toward the center. Brush the tortillas with the remaining tablespoon of oil. Place a sheet pan on top of the quesadillas (to help them hold their shape).
7. Bake until the tortillas start to get crispy, about 20 minutes. Remove the baking sheet from on top and continue baking for an additional 15 minutes.
8. Slice into rectangles and serve with salsa.