Using spiralizer, cut zucchini into ⅛-inch-thick noodles, then cut noodles into 12-inch lengths. (You should have 1 pound zucchini noodles after spiralizing; reserve any extra noodles for another use.)

Adjust oven rack to middle position and heat oven to 375 degrees. Add ground beef, 2 tablespoons pesto, ¼ teaspoon salt, and pepper flakes to large bowl and knead with your hands until well combined. Pinch off and roll mixture into 1¾-inch meatballs (you should have 6 meatballs).

Toss zucchini with oil, pepper, and remaining ¼ teaspoon salt on rimmed baking sheet and spread into even layer. Roast for 5 minutes. Push zucchini to sides of sheet, arrange meatballs in center, and roast until zucchini is tender and meatballs are cooked through, 10 to 15 minutes.

Remove zucchini and meatballs from oven. Transfer zucchini to colander and shake to remove any excess liquid. Toss zucchini with 1 tablespoon pesto in bowl, then divide among individual serving bowls. Top with meatballs, tomatoes, Parmesan, and remaining 2 tablespoons pesto. Serve.