In large cast iron pan, brown crumbled chorizo over medium heat until cooked through, 15 minutes, stirring occasionally.
Add red pepper and carrot, stir. Cook for about 5 minutes, and then add the onion and garlic. Cook an additional 20 minutes stirring occasionally to soften vegetables.
Add tomato paste, stir to coat vegetables, then add diced tomatoes, paprika, cumin, and parsley, simmer for additional 10 - 15 minutes.
Make wells in sauce with a tablespoon, and crack eggs into wells. Broil on high 4 - 8 minutes, depending on how you like your eggs. We love runny eggs, so I only cooked mine for 4 minutes!
Serve immediately, garnish with cojita cheese (optional)