1 tablespoon fresh chives, finely chopped, for garnish
Salsa, to top
In a large, heavy bottomed skillet over medium heat, add the chorizo and break up with a wooden spoon. Cook until browned and cooked through, about 10 minutes. Remove from the skillet and set aside.
Add the pepper and onion to the skillet and cook in the chorizo grease until the onions are translucent, approximately 5 minutes. Remove the vegetables using a slotted spoon and set aside with the chorizo.
If there is not enough grease left in the pan, add a tablespoon of oil. Add in the potatoes and season with salt and pepper. Cook, stirring every few minutes, until the potatoes are golden and crisp. Add the vegetables and chorizo back in with a slotted spoon, making sure not to add too much of the grease back to the pan with them. Add in the drained green chiles and stir.
Continue to cook 5-10 more minutes, or until the potatoes are tender and cooked through. Add in the cheese and stir.
Make two holes in the potato mixture and crack an egg into each well. Season with additional salt and pepper, and cook the eggs to your liking. (I covered the pan and cooked for about 4-5 minutes.)
Add on your salsa, avocado, and chives and serve immediately!