Heat a large cast-iron skillet. Add the garlic cloves and cook over moderate heat until slightly softened and just beginning to blacken all over, about 5 minutes. Add the tomatoes and onion to the skillet and cook until slightly softened and charred all over, about 7 minutes longer. Peel the garlic and transfer the vegetables to a food processor; add the chipotle and cilantro and pulse until still slightly chunky.
Reheat the skillet. Add the salsa and cook over moderately high heat, stirring often, until slightly thickened, 3 to 4 minutes. Season with salt and keep warm.
Preheat the oven to 350°. Heat 1/4 cup of the oil in a large skillet until shimmering. Using tongs, dip both sides of a tortilla into the hot oil and cook just until softened, about 10 seconds; let any excess oil drip back into the pan. Drain on paper towels and set the tortilla on a work surface. Repeat with the remaining tortillas. Spoon 1 1/2 tablespoons of the cheese onto each tortilla, then loosely roll them up and arrange side by side in a 9-by-13-inch baking dish. Sprinkle with the remaining 3/4 cup of cheese and bake for about 10 minutes, or until the enchiladas are warmed through and the cheese is melted.
Heat the remaining 2 tablespoons of oil in a nonstick skillet. Fry the eggs sunny-side up for 3 to 4 minutes. Arrange 2 enchiladas on each plate and top with the warm salsa and fried eggs.