Make the chips: Heat 3/4 inch vegetable oil in a pot over medium heat until a deep-fry thermometer registers 375 degrees F. Fry the tortillas in batches until golden, about 1 minute. Drain on paper towels and sprinkle with 1 tablespoon dressing mix.
Make the sauce: Heat a large skillet over medium-high heat. Add the tomatoes, onion and garlic and cook, turning, until the vegetables are charred, 5 to 7 minutes. Squeeze the garlic from its skin and cut the onion and tomatoes into chunks. Transfer to a blender; pulse with remaining dressing mix (about 2 tablespoons), the chipotles and half of the beans until smooth.
Heat the olive oil in the same skillet over medium heat. Add the pureed mixture and the remaining beans and cook until thick, about 5 minutes. Keep warm.
Make the eggs: Melt 1 teaspoon butter in a skillet over medium heat. Fry the eggs in batches until the whites are set, adding more butter as needed. Divide the sauce among shallow bowls; top each serving with 2 eggs, some ranch chips and avocado. Sprinkle with cilantro and cheese, if desired.