Cook pasta in a large pot of boiling salted water until very al dente, about 2 minutes less than package directions. Drain, reserving about 1 cup pasta water.
Meanwhile, heat olive oil in a Dutch oven or heavy pot over medium-low. Add onion, garlic, a large pinch of salt, and pepper. Cook, stirring often, until onion is softened and translucent, 8–10 minutes.
Add zucchini and cook until tender, about 5 minutes. Add asparagus, broccoli, peas, heavy cream, reserved pasta, and ½ cup pasta water. Cook, stirring often, until asparagus is tender and cream clings to pasta, about 5 minutes. Remove from heat.
Add Parmesan, basil, lemon juice, and butter. Stir vigorously, adding more pasta water as needed, until cheese is melted and sauce is smooth and glossy. Divide among bowls and top with more basil.