1Preheat the oven to 400F. Set a cooling rack over a baking sheet.
2Arrange the tortilla strips on the rack and coat with cooking spray. Sprinkle with the Mexi-Rub and bake until golden and crisp, 7-8 minutes.
3(if making this to serve on COOKDAY, leave the oven on. If making this for later in the week, you'll bake the casserole on the night of.)
4Spread the tomatoes in the bottom of a 9 by 13-inch baking dish. Scatter the black beans over the tomatoes. Top with the tortilla strips. Layer on the chopped beef and top with the cheeses.
5(Make-ahead: Let cool and refrigerate.)
(Night of: Return the casserole to room temp while you preheat the oven to 400F.)
6Bake until bubbling and browned on top, 10-15 minutes.
7Meanwhile, in a skillet or on a griddle, cook the eggs in butter to each person's liking.
Serve each portion of chilaquiles with a fried egg on top.
Garnish with cilantro, sliced chiles, and a lime wedge.