Preheat the oven to 400°F and line a baking sheet with parchment paper.
Shred the zucchini, then use a clean dish towel or paper towel to squeeze out all excess moisture. Place in a large bowl.
In the same bowl, mix the ground chicken, breadcrumbs, egg, Parmesan, garlic powder, Italian seasoning, salt, and pepper. Do not overmix. Form into 20 meatballs and place on the prepared sheet, evenly spaced.
Bake the meatballs for 15-18 minutes or until a meat thermometer reads 165°F.
While the meatballs are baking, melt butter in a large skillet over medium heat. Add shallots, garlic, and sundried tomatoes. Sauté until fragrant, about 2 minutes.
Pour in the white wine and let it reduce by half, about 2 minutes. Stir in the chicken broth and cream, letting it simmer gently for 2 minutes.
Add Parmesan and spinach, stirring until the spinach wilts.
Transfer the meatballs to the skillet, spoon sauce over them, and simmer for 3-5 minutes. Add extra broth if the sauce thickens too much.
Sprinkle with additional Parmesan, lemon zest, and basil before serving over pasta or with crusty bread.