Preheat your oven to 300 degrees. In a large (4-quart) pot, heat the oil over medium-high. Add about 2/3 of the onion and cook, stirring regularly, until richly browned, 8 to 10 minutes. Add the salsa and broth and bring to a rolling boil. Turn off the heat and stir in 2/3 of the shredded cheese.
Pour the chips into a 13x9 inch baking dish and cover with the sauce, gently pressing the chips into the sauce, breaking up larger pieces, so that all of the chips are coated. Sprinkle with the remaining 1/3 of the shredded cheese. Cover the baking dish with foil, being careful not to let the top of the chips touch the foil. Slide into the hot oven to heat through, 8 to 10 minutes. When the chilaquiles are bubbling, remove from the oven, drizzle with the crema and sprinkle with the remaining onion. Top with the queso aňejo and cilantro, and the optional sunny side up eggs. Serve without hesitation.