Heat oil or ghee in a large skillet that has a tight tting lid) over medium-high heat, uncovered.
Add onion and cook for about 4 minutes, until soft. Add garlic and cook an additional minute. Add all the peppers for about 5 minutes, until they are softened. Add cumin, paprika, oregano and salt and cook for one minute more.
Pour in tomatoes and water and bring to a simmer. Reduce heat to medium-low and continue to simmer sauce for 15 minutes, stirring occasionally.
Make 6 indentations in the sauce and crack an egg into each. Cover the pot and cook for 4-6 minutes, depending how you like your eggs.
Sprinkle on sesame seeds, parsley, and a dash of pepper. If serving with tortillas or brown rice, simply spoon over each. Otherwise, divide into bowls and enjoy.