Cook chorizo in a large frying pan over high heat, breaking up chunks with a spoon and stirring occasionally, until cooked through, about 6 minutes (to keep it from sticking, you may need to add a little water and turn down the heat). With a slotted spoon, lift chorizo from any oil and put in a bowl; set aside.
Add enough oil to pan to make about 2 tbsp. fat. Add onion and pepper and cook over medium heat, stirring occasionally, until onion is beginning to brown, about 10 minutes. Return chorizo to pan and stir in beans.
With a wooden spoon, make a well in the center. Crack eggs into well, sprinkle with salt and pepper, and let cook undisturbed 15 seconds; then use a spatula to softly scramble. Fold eggs into the chorizo-bean mixture. Top with cilantro and cheese and serve with tortillas and hot sauce.
*Avoid the very soft type sold in plastic casings; it doesn't taste great and tends to dissolve when cooked. To warm tortillas, wrap in a kitchen towel and microwave them for 1 minute.
Note: Recipe will be gluten free with gluten-free chorizo.