Heat the oil in a medium skillet over medium heat. Once hot, add the chorizo and cook until browned, about 3 minutes, stirring occasionally.
Add the celery, zucchini, bell pepper, and onion; turn the heat up to medium-high and cook until the veggies are softened, but not mushy, about 5 minutes, stirring frequently.
Add the garlic, turn the heat down to medium, and cook 1 minute, stirring constantly.
To serve, divide the hash between 2 plates. Top each with a fried egg and half of the cheese.