2. Heat oil in a 10- or 12-inch ovenproof skillet over medium heat. Add potatoes; cover and cook 8 minutes, turning every 2 minutes, until potatoes are almost tender. Stir in sausage. Heat thoroughly. Make 4 nests in potatoes.
3. Break an egg into each nest; season with salt and pepper. Cook 1–2 minutes or until eggs begin to set. Transfer skillet to oven. Bake 6–9 minutes or until eggs are set. Sprinkle with cheese; return to oven until cheese melts, about 1 minute.