Cook the bucatini pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.

In a large skillet over medium heat, add the olive oil. Once hot, add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.

Pour in the heavy cream and vegetable broth, stirring to combine. Bring the mixture to a gentle simmer.

Add the frozen peas and asparagus to the skillet. Cook for about 5-7 minutes, or until the asparagus is tender and bright green.

Stir in the lemon zest, salt, and pepper. Gradually add the grated Parmesan cheese, stirring until melted and creamy.

Add the cooked bucatini to the skillet, tossing to coat the pasta in the sauce. If the sauce is too thick, add a little reserved pasta water until the desired consistency is reached.

Serve immediately, garnished with fresh parsley.