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 3-4 minutes.
Stir in the minced garlic, dried oregano, dried basil, and crushed red pepper flakes; cook for 1 minute until fragrant.
Pour in the crushed tomatoes and chicken broth, stirring to combine.
Add the dry ziti pasta, salt, and black pepper to the pot. Stir well to submerge the pasta in the liquid.
Bring the mixture to a boil, then reduce heat to medium-low, cover, and simmer for 15 minutes, stirring occasionally to prevent sticking.
Remove the lid and continue cooking uncovered for an additional 5 minutes until the pasta is tender and most of the liquid is absorbed.
Remove the pot from heat and sprinkle the shredded mozzarella and grated Parmesan evenly over the top.
Cover the pot again and let it sit for 3-5 minutes to allow the cheese to melt.
Garnish with chopped fresh parsley before serving.