Heat the oven to 400°F. Put a 10-inch oven-safe skillet on the stove and set out a plate for the cooked chorizo.

Add the olive oil to the skillet and heat it over medium heat.

Add the chorizo to the skillet. Cook for 4 to 5 minutes, breaking it into small pieces with a wooden spoon, until it is browned and no longer pink.

Use a slotted spoon to transfer the chorizo to the plate. Leave about 1 tablespoon of fat in the skillet, and carefully pour off any extra.

Add the chopped onion to the skillet. Cook for 4 minutes, stirring often, until it softens and starts to brown at the edges.

Add the garlic and cumin to the skillet. Stir for about 30 seconds, just until they smell fragrant.

Add the drained hominy and the green chiles to the skillet.

Stir the hominy mixture well so the kernels get coated in the seasoned fat and onions.

Cook for 3 to 4 minutes, stirring once or twice, until the hominy is hot and a few kernels pick up light brown spots.

Return the cooked chorizo and any juices from the plate to the skillet. Stir to combine everything evenly.

Taste a spoonful of the hominy mixture and season it with the salt and black pepper. Keep in mind that the cheese will add a little more salt.

Use the back of a spoon to make 4 shallow spaces in the mixture for the eggs.