Cook and stir turkey and rosemary sprig with olive oil in a large, deep skillet over medium heat until turkey renders its fat but is not crisp, about 5 minutes. Add inion and Mushroom and sauté with the meat and add salt and pepper for another 5 minutes. Now add the pasta sauce and keep stirring for another 5-8 minutes.

Fill a large pot with salted water and bring to a boil. Stir in penne and return to a boil. Cook pasta, stirring occasionally, until cooked through but still chewy, about 10 minutes; drain and return to pot.

Pour sauce over penne and stir to combine. Turn off heat, cover pot with a lid, and let stand 5 minutes for pasta to absorb sauce. Serve sprinkled with cheese.