Preheat the oven to 375 degrees F. Heat the olive oil in a large ovenproof skillet over medium-high heat. Add the onion, season with salt and cook, stirring frequently, until lightly browned, 5 minutes. Add the garlic and cook, stirring, 2 minutes. Add the hominy, salsa and 3/4 cup water. Bring to a boil, then reduce the heat to a simmer and cook until thickened, about 5 minutes.
Add the kale in batches, stirring after each addition to wilt the greens. Season with 3/4 teaspoon salt and a few grinds of pepper. Remove from the heat.
Make 8 indentations in the mixture with the back of a large spoon and crack an egg into each well. Season with salt and pepper and top with the cheese. Transfer the skillet to the oven and bake until the egg whites are set, about 11 minutes. Top with cilantro. Serve with tostadas.
Photograph by Ryan Dausch