Cook the fettuccine or spaghetti according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Pour in the heavy cream and stir to combine. Bring the mixture to a gentle simmer.
Gradually whisk in the grated Parmesan cheese until melted and smooth. If the sauce is too thick, add a little reserved pasta water until you reach your desired consistency.
Season the sauce with salt, black pepper, and red pepper flakes if using. Stir to combine.
Add the cooked pasta to the skillet and toss to coat in the creamy sauce. Cook for an additional 1-2 minutes to heat through.
Serve immediately, garnished with chopped fresh parsley.