In a large pot, bring salted water to a boil. Add the fettuccine and cook according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain and set aside.
In a large skillet over medium-high heat, add olive oil. Once hot, add the shrimp and season with salt, pepper, and red pepper flakes if using. Cook for 2-3 minutes on each side until the shrimp are pink and opaque. Remove the shrimp from the skillet and set aside.
In the same skillet, lower the heat to medium, and add the minced garlic. Sauté for about 1 minute, or until fragrant but not browned.
Pour in the heavy cream and stir to combine. Allow it to simmer for about 2-3 minutes, then add the grated Parmesan cheese. Stir until the cheese has melted and the sauce is creamy. If the sauce is too thick, add some reserved pasta water to reach your desired consistency.
Return the shrimp to the skillet and toss to coat in the creamy sauce. Add the cooked pasta and lemon zest, mixing everything together until well combined. Season with additional salt and pepper as needed.
Divide the creamy garlic shrimp pasta into serving bowls and garnish with fresh parsley and extra Parmesan if desired.