In a large pot or deep skillet, heat olive oil and butter over medium heat until melted.
Add the minced garlic and sauté for 1 minute until fragrant, stirring frequently to avoid burning.
Add the linguine pasta, vegetable broth, and water to the pot. Stir to combine and ensure the pasta is submerged.
Bring the mixture to a boil over high heat, then reduce to medium-low heat and simmer uncovered, stirring occasionally, until the pasta is al dente and most of the liquid is absorbed, about 10-12 minutes.
Stir in the heavy cream, grated Parmesan cheese, lemon zest, lemon juice, salt, and black pepper.
Cook for an additional 2-3 minutes, stirring frequently, until the sauce is creamy and coats the pasta evenly.
Remove from heat and sprinkle chopped fresh parsley over the pasta.
Serve immediately, garnished with extra Parmesan if desired.