Preheat flat grill or a nonstick skillet over medium-high heat.
Add the vegetable oil, potatoes, diced onion, green pepper, jalapeno pepper, if using, and.
chorizo. Mix together slightly. Cook for 4 to 8 minutes, flipping once. Add the tomato and eggs. Mix together and cook for another 2 to 3 minutes, flipping over once. Add cheese and cook until slightly melted. Mix hash together to distribute cheese and tomatoes throughout.