Preheat the oven to 425 degrees F.
Toss together the sausage, oregano, red pepper flakes, garlic, bell peppers, onion, 1 tablespoon of the olive oil, 1 teaspoon salt and a few grinds of black pepper on a sheet pan. Pour the cherry tomatoes over top and gently shake the pan a few times to evenly distribute. Bake until the sausage is cooked through and the vegetables are soft, 18 to 20 minutes.
Meanwhile, toss the gnocchi with the Parmesan, remaining 1 tablespoon olive oil and 1/2 teaspoon salt.
Turn the oven to broil. Sprinkle the gnocchi over the sausage and vegetables and broil until dark golden brown, 3 to 5 minutes. Divide among 4 plates and sprinkle with the parsley and more Parmesan.
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