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Arrange a rack in the middle of the oven and heat to 450°F and line a rimmed baking sheet with foil
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Place the gnocchi, peppers, tomatoes, onion, garlic, rosemary, salt, and pepper in a large bowl. Drizzle with the oil and gently toss to combine. Spread the gnocchi mixture out evenly on the prepared baking sheet.
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Roast, stirring halfway through, until the gnocchi are plump and the vegetables are tender and caramelized, 18 to 20 minutes total.
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To serve, spoon the gnocchi and vegetable mixture into individual bowls and garnish each bowl with the basil and grated cheese, if using.