In a large bowl, whisk the eggs and 2 tablespoons water vigorously. Set aside.
Heat the butter and oil in a large skillet over medium-high heat. Once the butter melts, add the tortilla strips and cook, stirring and tossing, until they are all golden and crispy.
When the tortillas are crisp, add the bell pepper, chilies and onion to the skillet. Season with a pinch of salt and little grinds of black pepper. Cook until tender, about 5 minutes.
Add the eggs to the pan, season with salt and reduce the heat to medium low. Cook, stirring to scramble and combine, until most of the moisture is cooked out, then remove from the heat. Stir in the tomatoes. Serve topped with cheese.