In a large bowl, whisk the eggs 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 golden and crispy, 2 to 3 minutes. Add the chiles and onion to the skillet. Season with a pinch of salt and a few 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, 2 to 3 minutes. Remove from the heat and stir in the salsa verde.
Serve topped with the cheese. Garnish with the avocado, cilantro, scallions and a drizzle of crema.