Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente.
While pasta cooks, heat olive oil in a large skillet over medium-high heat.
Sauté the onion and carrot for 2 minutes until slightly softened.
Add the broccoli, zucchini, and bell pepper; cook for 5 minutes until tender-crisp.
Stir in the minced garlic and frozen peas, cooking for an additional 1 minute.
Reduce heat to low and stir in the heavy cream and half of the Parmesan cheese.
Drain the pasta, reserving 1/2 cup of pasta water.
Toss the pasta with the vegetable mixture, adding reserved pasta water if needed to loosen the sauce.
Stir in lemon juice, salt, pepper, and remaining Parmesan.
Garnish with fresh parsley and serve immediately.