Heat olive oil in a large pot or deep skillet over medium heat.
Add diced onion and cook, stirring occasionally, until softened and translucent, about 5 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Pour in crushed tomatoes and vegetable broth, stirring to combine.
Add dried basil, dried oregano, salt, black pepper, and red pepper flakes to the pot. Stir well.
Add dry ziti pasta to the pot, making sure the pasta is submerged in the liquid.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered, stirring occasionally, until the pasta is tender and most of the liquid is absorbed, about 15 minutes.
Remove the pot from heat and stir in grated Parmesan cheese until melted and combined.
Sprinkle shredded mozzarella cheese evenly over the pasta. Cover the pot with a lid and let it sit for 2-3 minutes until the cheese melts.
Garnish with chopped fresh parsley and serve immediately.