Blitz eggs, cheese, 2 tablespoons of parsley, remaining salt, freshly-ground pepper, cubanelle, and onion in the food processor until the onion and cubanelle are finely chopped.
Remove from the heat and cool for five minutes before serving.Pour the queso cremita mixture into the skillet. Top with cheddar. Cover with a tight-fitting lid and cook over very low heat for 15 minutes, the cheddar should be completely melted, cover and cook for another 5 minutes if it isn't.