In a bowl, beat eggs with the milk and cheese. Season with salt and pepper to taste.
Heat a skillet to medium heat. Cook the onions until translucent, 3-4 minutes. Turn heat down to low and wait a few minutes to allow the pan to cool down. Melt the butter and olive oil. Add the eggs and cook slowly, gently pushing the eggs around when they start set at the bottom. Transfer eggs to a plate and keep warm with foil.
Cook the chorizo in a skillet over medium heat until cooked through and browned.
Warm tortillas on open flame or microwave. See Kitchen Tips above.
To assemble, place some eggs and chorizo on each tortilla. Top with diced tomatoes, diced onions, cheese, avocado slices, cilantro, a little squeeze of lime juice, and jalapeños (if using).