Heat a skillet over medium heat; add 1 tablespoon of olive oil. When olive oil ripples, add salsa and cook over medium heat, stirring occasionally for about 10 minutes.
Meanwhile, begin warming beans in a separate pan.*
Transfer cooked salsa to bowl; cover to keep warm.
Wipe out skillet; heat skillet over medium heat. Add tortillas in single layer to dry skillet (working in batches as needed), cook until warm and slightly toasted, turning as needed. Remove and cover to keep warm.
Heat skillet over medium heat. Coat pan with a bit of butter. Fry eggs to preference; season to taste with salt and pepper. Add additional butter as needed.
Serve fried eggs on warm tortillas, topped with cooked salsa, warmed black beans, and cheese. Add any optional chopped fresh cilantro, sliced/diced avocado or avocado, sliced jalapeno or fresh corn as desired.