Scrub potatoes and dice into 1/4-inch pieces (peeled or unpeeled).
Heat oil in a 10-inch cast-iron skillet over medium-high heat. Put minced garlic into the skillet and let brown for 2-3 minutes. Add the potatoes and season with cumin, chili, salt and pepper. Sauté 8-10 minutes.
Reduce heat to medium. Add beans to the skillet and sauté 2-3 minutes along with the potatoes. Create space for the sausage patties by pushing beans and potatoes to the sides. Cook 5 minutes on one side before flipping over. Sprinkle fresh corn around the skillet.
Using a spatula, create 4 divots in the mixture and crack 1 egg into each divot. Continue cooking on the stove until the egg whites are set (yolks can still be runny) another 5-8 minutes.
Remove the skillet from the stovetop and sprinkle tortilla strips over the top. Serve with salsa or pico de gallo.