In a large pot or deep skillet, combine the linguine pasta, vegetable broth, water, olive oil, minced garlic, salt, black pepper, and red pepper flakes.
Bring the mixture to a boil over medium-high heat, stirring occasionally to prevent the pasta from sticking.
Reduce the heat to medium and simmer, stirring frequently, until the pasta is cooked al dente and most of the liquid is absorbed, about 10 to 12 minutes.
Stir in the fresh lemon juice, lemon zest, heavy cream, and unsalted butter until the butter is melted and the sauce is creamy.
Add the grated Parmesan cheese and stir until melted and fully incorporated into the sauce.
Taste and adjust seasoning with additional salt, pepper, or lemon juice if desired.
Remove from heat and sprinkle the chopped fresh parsley over the pasta.
Serve immediately, garnished with extra Parmesan cheese if desired.