Preheat oven to 350 degrees. Lightly spray bottom of a 9x13-inch baking dish with cooking spray.

Bring a large pot of lightly salted water to a boil. Add penne pasta and cook until al dente, about 8 minutes. Drain.

Heat a large skillet over medium heat; cook and stir onion and carrot until onion is translucent and carrot is crisp-tender. Add the pound of turkey. Cook until it is no longer pink, about 7 minutes. Add spaghetti sauce and simmer until heated through, about 5 minutes.

Layer ingredients into prepared baking dish as follows: half the cooked penne pasta, provolone cheese, sour cream, half the sauce mixture, remaining penne, mozzarella cheese, and remaining sauce mixture. Top with grated Parmesan cheese.

Bake in preheated oven until cheeses are melted, about 30 minutes.