Heat a large skillet over medium high heat. Add the chorizo and break into small pieces with a spoon, stirring often, until cooked through and lightly browned, about 8 minutes. Remove the chorizo from the pan and set aside.

Wipe out the skillet and return to the heat, adding the vegetable oil. Add the potatoes and onion powder, saute, stirring often, until potatoes are cooked through and crispy. Add the chorizo back to the pan.

Turn the heat down to medium/low. Make four indentations in the mixture, break an egg into each one, cover the skillet, and cook just until the eggs are set, about 5 minutes.