Place the tomatillos in a large pot and cover with cold water. Bring to a boil, and boil for 5 minutes. Drain, and transfer to the bowl of a food processor fitted with a metal blade. Add the onion, jalapeno, cilantro, garlic, lime juice, cumin, garlic powder, and onion powder. Puree until completely blended. Set aside.
Add the oil to a small frying pan and heat over medium heat. One at a time, fry each corn tortilla in the pan for 1 1/2 minutes on each side. Transfer to a surface lined with paper towels to drain. Continue until all tortillas are done.
In a large skillet over medium heat, melt the butter. Crack the eggs into the the pan and cover. Cook until set. Sprinkle with salt and pepper.
To serve, set a tortilla on each plate. Top with tomatillo sauce, then a generous spoonful of the beans, an egg, then the crumbled cheese. Enjoy.