In a large cast-iron or other heavy skillet, saute onion, green pepper and garlic in oil until tender. Stir in tomatoes, jalapeno and seasonings; simmer, uncovered, for 15 minutes. Make 6 indentations in the tomato mixture with a spoon. Break eggs into indentations.
Cover and cook on low heat until eggs are set, 5 minutes. Sprinkle with cheese; cover and cook until melted, about 1 minute. If desired, serve with tortillas.
Wear disposable gloves when cutting hot peppers; the oils can burn skin. Avoid touching your face.