Preheat oven to 375°F (190°C).
Make the sauce: Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 7-8 minutes. Add garlic and cook for one minute more, until fragrant.
Stir in diced tomatoes, crushed tomatoes, vegetable broth, oregano, basil, salt, and pepper. Bring to a simmer and cook for 15 minutes, stirring occasionally.
Cook the vegan sausage: In a separate skillet, cook the crumbled vegan sausage over medium heat until browned.
Make the cashew ricotta: Drain the soaked cashews and rinse under cold water. In a blender, combine the cashews, water, nutritional yeast, lemon juice, garlic powder, salt, and pepper. Blend until smooth and creamy.
Assemble the ziti: Cook the ziti according to package directions. Drain and set aside.
In a large bowl, combine the cooked ziti, sauce, cooked vegan sausage, cashew ricotta, vegan mozzarella cheese shreds, and parsley. Toss to coat evenly.
Transfer the ziti mixture to a greased 9x13-inch baking dish.
Bake for 20-25 minutes, or until heated through and bubbly.
Let stand for 10 minutes before serving.