Preheat your oven to 400°F (200°C). Line a rimmed baking sheet with parchment paper or lightly oil it.
Prepare the vegetables.
Grate the zucchini and carrot on the small holes of a box grater. Place the grated zucchini in a clean kitchen towel and squeeze out as much liquid as possible. Finely mince or grate the onion.
In a large bowl, combine the ground turkey, zucchini, carrot, onion, garlic, breadcrumbs, Parmesan, egg, parsley, Italian seasoning, smoked paprika (if using), salt, and pepper.
Mix gently with a fork or your hands until just combined. Do not overmix or the meatballs can become dense.
Lightly oil your hands.
Scoop about 2 tablespoons of the mixture per meatball and roll into balls. You should get 18–22 meatballs, depending on size.
Place meatballs on the prepared sheet. Brush or mist lightly with olive oil for better browning.
Bake for 14–17 minutes, or until the centers reach 165°F (74°C).
For extra color, broil for 1–2 minutes at the end, watching closely.
Serve warm with your favorite sauce or sides. For a classic route, simmer gently in warm marinara for 3–5 minutes before serving to soak up flavor.