Heat a large cast iron skillet with olive oil over high heat. Add onions and spices and saute until onions are translucent (3-4 minutes).
Add chorizo and green chiles to the pan, stir and cook for 5-6 minutes until chorizo is browned.
Reduce heat to medium and add the red potatoes to the pan and stir to mix. Pour 1/4 cup of water to the pan and cover with a lid to steam the potatoes. Uncover and stir occasionally to loosen cooked on bits of food.
Once potatoes have softened and browned, make shallow divots for the eggs. Crack eggs into divots, cover and continue to cook for another 3-5 minutes (you want the egg whites set but yolk runny). Sprinkle with shredded cheese.
Serve and top with desired toppings.
Recipe for fresh pico de gallo, can be found here: Pico de Gallo.