Heat olive oil in a large deep skillet or Dutch oven over medium heat.
Add the Italian turkey sausage, breaking it up with a spoon, and cook until browned and cooked through, about 5-7 minutes.
Add the diced onion to the skillet and cook until softened, about 3 minutes.
Stir in the minced garlic and cook for 1 minute until fragrant.
Pour in the crushed tomatoes, tomato sauce, and chicken broth. Stir to combine.
Add the dried oregano, dried basil, crushed red pepper flakes, salt, and black pepper. Stir well.
Add the uncooked ziti pasta to the skillet and stir to submerge the pasta in the sauce.
Bring the mixture to a boil, then reduce heat to low. Cover and simmer for 15 minutes, stirring occasionally, until the pasta is tender and most of the liquid is absorbed.
Remove the lid and stir the pasta. Sprinkle the shredded mozzarella cheese and grated Parmesan cheese evenly over the top.
Cover again and cook for an additional 3-5 minutes until the cheese is melted.
Remove from heat and sprinkle chopped fresh parsley over the top before serving.