Preheat oven to 400°F and line a large sheet pan with foil.
Toss potatoes, sausage coins, bell peppers, and onion with olive oil, garlic powder, smoked paprika, salt, and pepper on the sheet pan.
Spread into a single layer and roast for 25 minutes, stirring once halfway through.
Use a spoon to create six wells in the mixture and crack one egg into each well.
Return to the oven for 8 to 10 minutes until egg whites are set but yolks are still slightly runny.
Scatter shredded cheddar over the top and serve directly from the pan.