Preheat your oven to 425°F (220°C) and line a baking sheet with parchment paper.
Dice the sweet potato into small cubes, slice the onion, and dice the red bell pepper.
Place the sweet potato, onion, and bell pepper in a bowl. Drizzle with olive oil and season with salt and pepper. Toss to coat evenly.
Spread the vegetable mixture onto the prepared baking sheet in a single layer.
Roast in the preheated oven for about 20-25 minutes, stirring halfway through, until the sweet potato is tender and slightly crispy.
While the vegetables are roasting, cook the turkey sausage in a skillet over medium heat until browned, about 5-7 minutes, then slice into bite-sized pieces.
In the last 5 minutes of the roasting time, create small wells in the hash and crack the eggs into them, or cook the eggs separately if desired. Bake until the egg whites are set but yolks remain runny, around 5 minutes.
Remove the sheet pan from the oven. Gently mix in the sliced turkey sausage, season with extra salt and pepper if needed, and serve immediately.