Arrange a rack in the middle of the oven and heat the oven to 375°F. Meanwhile, peel and cut 1 pound potatoes into 1-inch pieces. Drain and rinse 1 can pinto beans. Remove the casings from 12 ounces breakfast sausage if needed.

Heat a 10-inch cast-iron skillet or ovenproof nonstick frying pan over medium-high heat. Add the sausage and cook, breaking it up into bite-sized pieces with a wooden spoon, until browned and cooked through, about 8 minutes. Using a slotted spoon, transfer the sausage to a paper towel-lined plate, leaving the fat in the pan.

Add the potatoes to the skillet and season with ½ teaspoon kosher salt and ¼ teaspoon black pepper. Cover and cook, stirring occasionally, until the potatoes are tender and can be easily pierced with a knife, about 10 minutes.

Add the beans, sausage, 1 cup salsa, and 1 cup of the shredded cheese. Stir to combine and bring to a simmer, then reduce heat to low. Sprinkle with the remaining ¼ cup cheese. Create 4 divots in the mixture with the back of a spoon. Crack 1 large egg into each divot.

Bake until the egg whites are set but the yolks are still runny, 10 to 12 minutes. Meanwhile, pit and slice 1 avocado. Coarsely chop ¼ cup fresh cilantro leaves.

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