
Cook the pasta according to package directions until al dente. Reserve about 1 cup of pasta water before draining.
While the pasta is cooking, heat olive oil in a large skillet over medium heat. Add garlic and cook until fragrant, about 1 minute.
Add asparagus, peas, and zucchini to the skillet. Cook for 5-7 minutes, or until vegetables are tender-crisp.
Stir in heavy cream, lemon juice, lemon zest, salt, and pepper. Bring to a simmer and cook for 2-3 minutes, allowing the sauce to slightly thicken.
Add the drained pasta to the skillet with the vegetables and sauce. Toss to coat. If the sauce is too thick, add a little of the reserved pasta water until it reaches your desired consistency.
Stir in the grated Parmesan cheese. Taste and adjust seasoning as needed.
Serve immediately, garnished with extra Parmesan cheese and fresh parsley, if desired.