In a large sauté pan, heat the olive oil and butter over medium-high heat. When the butter is melted and beginning to fizz, add the onion, salt and pepper and cook until it’s just beginning to soften, 3 to 4 minutes. Add the diced sweet potato to the pan. Without stirring, cook the sweet potato until the first side is just browned, about 4 minutes. Toss and stir well, redistributing, and cook for another 2 minutes without stirring. Add the apple to the pan and cook, stirring often, until it’s just softening and is warmed through. By adding ingredients to the pan slowly, you’ll get sweet and nicely caramelized onion, crispy sweet potato, and just-cooked apple that will maintain its shape and texture.

Reduce the heat to medium-low and make four 2-inch-wide wells in the sauté pan. To do this, push the vegetables aside with a spoon. Make sure the pan still has a bit of grease (add some butter to each well, if needed), crack 1 egg into each well and cover for two minutes for soft yolks, four minutes for hard yolks. Serve with toast, or not!

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