Preheat the oven to 300 degrees . On a baking sheet, bake the tortillas in one layer until golden, 15 minutes.
Meanwhile, in a large skillet, heat 2 tbsp. oil over medium-high. Add the onion and cook, stirring often, until lightly browned, 8 to 10 minutes.
In a blender, puree the salsa, tomatoes, chipotle and adobo sauce. Transfer to the skillet, add the beans and cook, stirring often, until warmed through, 5 minutes; season with salt and pepper.
In a large nonstick skillet, heat the remaining 1 tbsp. oil over medium-high. Fry the eggs sunny-side up until the whites are just set, about 3 minutes; season. Stir the tortillas into the black bean sauce. Divide among bowls and sprinkle with the cheese. Top each bowl with an egg. Garnish with cilantro and lime wedges.