Preheat the oven to 375 degrees. Bring a large pot of salted water to a boil and cook the ziti until al dente. Drain and set aside.
Heat the olive oil in a large skillet over medium heat. Add the onion, celery, and carrots. Cook for 5 to 7 minutes until the vegetables begin to soften.
Stir in the garlic and cook for 1 minute. Add the ground turkey, breaking it up with a spoon. Cook until the meat is no longer pink.
Season the mixture with oregano, salt, and pepper. Pour in the marinara sauce and simmer for 5 minutes to blend the flavors.
Spread a thin layer of the sauce mixture in a 9 by 13 inch baking dish. Add half the cooked ziti, dollops of ricotta, and a sprinkle of mozzarella. Repeat the layers and finish with the remaining mozzarella and Parmesan on top.
Bake uncovered for 20 to 25 minutes until the cheese is melted and lightly browned.