Heat the olive oil in a large, non-stick skillet over medium-high heat. Add the chorizo and cook, breaking it up with a spatula, until browned and cooked through, about 5-7 minutes. Drain off most of the grease, leaving about a tablespoon in the skillet.
Add the diced onion and bell peppers to the skillet with the chorizo. Cook, stirring occasionally, until the vegetables are softened, about 5-7 minutes.
Stir in the diced cooked potatoes, cumin, chili powder, salt, and pepper. Cook for another 3-5 minutes, stirring to combine and allowing the potatoes to heat through and get slightly crispy.
Create four wells in the mixture using your spatula. Crack one egg into each well. Reduce the heat to medium-low, cover the skillet, and cook until the egg whites are set but the yolks are still runny, about 5-8 minutes, depending on how you like your eggs.
Remove the lid and sprinkle the shredded cheese over the top of the skillet. Cover for another minute or until the cheese is melted.
Garnish generously with your favorite optional toppings like fresh cilantro, avocado, salsa, and a dollop of sour cream or a dash of hot sauce before serving.