Heat the oven to 375°F. Line a small rimmed baking sheet or loaf pan with parchment paper.
In a large bowl, combine the ground turkey, pesto, breadcrumbs, egg, 2 tablespoons of the Parmesan, salt, and black pepper. Mix gently until just combined.
Shape the mixture into a compact loaf on the prepared baking sheet, or press it into the loaf pan. Bake until the center reaches 165°F, about 40 to 50 minutes. Let the meatloaf rest for 5 minutes before slicing.
While the meatloaf bakes, bring the water to a boil in a medium saucepan. Slowly whisk in the polenta. Reduce the heat to low and cook according to the package directions, stirring often, until thick and creamy.
Remove the polenta from the heat. Stir in the butter and the remaining 2 tablespoons of Parmesan.
Spoon the polenta onto plates and serve with slices of pesto turkey meatloaf.