Heat oven to 425 degrees.
In a large bowl, stir together olive oil, garlic, oregano, salt and chile flakes. Add gnocchi, onion, peppers and tomatoes, and toss well. Spread evenly on a large rimmed baking sheet. Nestle the sausages among the vegetables.
Roast for 35 to 40 minutes, stirring everything and flipping the sausages after 15 minutes, until the sausages are cooked through and the vegetables and gnocchi are golden brown.
Top with Parmesan and basil. Sprinkle more chile flakes if you like. Serve warm.
