Cook the Pasta: Bring a large pot of salted water to a boil. Cook the pasta according to the package instructions until al dente. Drain and set aside.
Make the Vegan Parmesan: Prepare Homemade Vegan Parmesan following the recipes in the notes.
Prepare the Sauce: Blend all the sauce ingredients until smooth. If it’s too thick, add a little more plant-based milk. Taste and adjust seasoning if needed.
Sauté the Veggies: In a large pan over medium heat, sauté the garlic, mushrooms, and broccoli with a splash of water or vegetable broth for about 5 minutes. Add the cherry tomatoes, oregano, basil, smoked paprika, salt, and pepper, and cook for another 2 minutes. Add the frozen peas and cook for one more minute until warmed.
Combine Pasta and Sauce: In a large mixing bowl, combine the cooked pasta, sautéed veggies, and the creamy sauce. Mix well to coat everything evenly.
Assemble and Bake: Preheat the oven to 375°F (190°C). Transfer the pasta mixture to a baking dish. Sprinkle Homemade Vegan Parmesan generously over the top.
Bake: Bake uncovered for 20-25 minutes or until the top is golden and slightly crispy.
Serve and Enjoy: Let it cool for a few minutes before serving. Garnish with fresh basil or parsley.