Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Drain and set aside.
In a large skillet, heat olive oil over medium heat. Add onion and garlic; sauté until softened. Add zucchini and mushrooms; cook until tender.
Stir in marinara sauce and heavy cream. Season with salt and pepper. Simmer for 3–4 minutes.
Preheat oven to 375°F (190°C). Toss cooked pasta with the sauce until evenly coated. Transfer to a lightly greased baking dish.
Sprinkle mozzarella and Parmesan evenly over the top. Bake uncovered for 20–25 minutes, or until the cheese is melted and golden.
Remove from oven and let cool slightly. Garnish with fresh basil, dill, and green onions before serving.