Heat oil in a large skillet over high heat. Add potatoes and cook until brown and crispy, stirring only as needed to prevent sticking, 8 to 10 minutes. Remove potatoes from the skillet and keep warm.
Place beef, carrots, onion, bell pepper, jalapeno, cumin, chili powder, garlic powder, salt, oregano, paprika, and black pepper into the same skillet. Cook until beef is browned and crumbly, 7 to 8 minutes. Stir in corn, tomatoes, and salsa. Cook for 3 to 4 minutes. Stir in cooked potatoes. Top with Cheddar cheese, cover, and reduce heat to medium. Cook until cheese melts, about 1 minute.