Arrange a rack in the middle of the oven and heat the oven to 375°F. Meanwhile, peel and cut the potatoes into 1-inch pieces. Drain and rinse the pinto beans. Remove the casings from the breakfast sausage if needed.

Heat a 10-inch cast-iron skillet over medium-high heat. Add the sausage and cook, breaking it up into bite-sized pieces until browned and cooked through, about 8 minutes. Transfer the sausage to a paper towel-lined plate, leaving the fat in the pan.

Add the potatoes to the skillet and season with salt and black pepper. Cover and cook, stirring occasionally, until the potatoes are tender, about 10 minutes.

Add the beans, sausage, 1 cup salsa, and 1 cup cheese. Stir to combine and bring to a simmer, then reduce heat to low. Sprinkle with remaining cheese. Create 4 divots in the mixture and crack an egg into each.

Bake until the egg whites are set but yolks are still runny, 10 to 12 minutes. Meanwhile, pit and slice the avocado and chop the cilantro.

Remove the skillet from the oven and top with avocado and cilantro. Serve with more salsa and optional tortilla chips or tortillas.