Heat the oven to 375°F. Line a rimmed baking sheet with parchment paper. Grate the zucchini, then squeeze it firmly in a clean kitchen towel to remove excess moisture.
In a large bowl, combine the ground turkey, squeezed zucchini, ½ cup quick-cooking polenta, Parmesan, egg, milk, tomato paste, Italian seasoning, garlic powder, salt, and black pepper. Mix gently until everything is evenly combined.
Shape the mixture into a compact loaf on the prepared baking sheet. Bake until the center reaches 165°F on an instant-read thermometer, about 45 to 55 minutes. Let the meatloaf rest for 10 minutes before slicing.
While the meatloaf rests, bring 4 cups of water and ½ teaspoon salt to a boil in a saucepan. Slowly whisk in 1 cup quick-cooking polenta. Reduce the heat and cook, stirring often, according to the package directions, until thick and tender. Stir in the butter.
Spoon the polenta onto plates and serve with slices of meatloaf.