Preheat the oven to 425°F and line a sheet pan with parchment paper. In a large bowl, combine the ground turkey, grated zucchini, breadcrumbs, egg, garlic, parsley, mint, oregano, half the salt, and half the pepper. Mix gently and form into 20 meatballs.
In another bowl, toss the sliced zucchini, eggplant, bell pepper, and cherry tomatoes with olive oil, balsamic vinegar, and the remaining salt and pepper. Spread the vegetables on the sheet pan and nestle the meatballs among them.
Roast for 20-25 minutes, until the meatballs reach an internal temperature of 165°F and the vegetables are tender. During the last 5 minutes, sprinkle the feta cheese over the vegetables.
Remove from the oven and let rest for 5 minutes before serving. These Mediterranean-spiced meatballs with their colorful vegetable accompaniment create a satisfying meal that's both healthy and delicious.