Preheat the oven to 450°F.
In a large bowl, combine the gnocchi, tomatoes, garlic, broccoli, bell peppers, red onion, salt, Italian seasoning, black pepper, and red pepper flakes. Pour the oil over the gnocchi and vegetables, tossing to coat.
Spoon the gnocchi onto a baking sheet. Bake until the gnocchi have begun to brown and crisp, 35 to 40 minutes, stirring halfway through. Remove the baking sheet from the oven and dot with the mozzarella balls. Bake until the mozzarella is melted, 5 minutes.
Remove the baking sheet from the oven and sprinkle with the basil. Serve hot over the arugula and sprinkled with parmesan, if you like.
