Warm tortillas in a cast iron skillet for a firm texture or microwave for 30 seconds for a soft texture. If made in advance and cold, warm refried beans in the microwave for 30 seconds and then spread about 2 tablespoons of beans onto each tortilla, divided among four plates. Place plates in the oven to keep warm. If made in advance and cold, warm sauce for 1 minute in the microwave to remove the chill and set aside.
Fry eggs once everything is ready to assemble. Melt 2 tablespoons of butter in a skillet over medium-low heat. When butter just starts to bubble, break eggs into the skillet (cooking two at a time will leave room to flip the eggs) and cook slowly until whites are almost set and yolk is still soft. For over-easy eggs, gently turn the eggs over in the skillet and cook briefly, or allow the white to fully set (sunny-side up).
Transfer eggs to top the bean-covered tortillas in the oven. Top with a bit of cheese and about 1/4 cup of sauce, as desired, and return to the oven. Repeat with remaining eggs.
Serve with a garnish of cilantro and extra sauce to pass at the table. Note: Plates will be hot to the touch so take care with young children.