Bring a large pot of salted water to a boil. Add the fettuccine pasta and cook according to package instructions until al dente, about 10-12 minutes. Drain the pasta and set aside.
In a large skillet over medium heat, melt the butter. Add the minced garlic and sauté for 1-2 minutes until fragrant, being careful not to brown the garlic.
Pour in the heavy cream and bring to a gentle simmer. Cook for 5 minutes, stirring occasionally, until the cream slightly thickens.
Reduce heat to low and gradually whisk in the grated Parmesan cheese until the sauce is smooth and creamy.
Season the Alfredo sauce with salt and freshly ground black pepper. Stir well to combine.
Add the cooked fettuccine to the skillet with the Alfredo sauce. Toss gently to coat the pasta evenly with the sauce.
Remove the skillet from heat and let the pasta cool to room temperature.
Transfer the pasta Alfredo to an airtight container. Cover and refrigerate for up to 2 days.
To reheat, place the pasta in a skillet over low heat. Add 2-3 tablespoons of milk or cream to loosen the sauce, stirring gently until heated through.
Garnish with chopped fresh parsley before serving.