In a large skillet, heat 1 tbsp of the olive oil. Brown the sausage over medium heat until cooked. Transfer to a plate.
Add remaining oil to the skillet. Add diced sweet potato, apple, onion and sage. Stir and place in preheated oven. Bake for 20-25 minutes, stirring every 10 minutes.
Add sausage back in to skillet and season with salt and pepper to taste. Make 4 holes for eggs, and gently crack an egg into each hole.
Place back in the oven until eggs are cooked as desired, 6-10 minutes.
Remove skillet from oven and divide hash between 4 bowls.