Preheat your oven to 400°F and line a large rimmed sheet pan with parchment paper.
Dice the sweet potato into small half-inch cubes and slice the chicken sausage into half-inch rounds.
Place the sweet potatoes, sausage, chopped bell peppers, and onions directly onto the prepared sheet pan.
Drizzle the mixture with olive oil and sprinkle with sea salt, black pepper, garlic powder, and smoked paprika.
Toss everything together until evenly coated, then spread into a single layer across the pan.
Roast for 20 minutes, tossing halfway through, until the potatoes are tender and the sausage is lightly browned.
Use a large spoon to create three small wells in the hash and carefully crack one egg into each well.
Return the pan to the oven for 5 to 8 minutes, or until the egg whites are fully set but the yolks remain soft.