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 and set aside.
In a large skillet over medium heat, melt the butter. Add the minced garlic and sauté for 1 minute until fragrant, being careful not to brown it.
Pour in the heavy cream and bring to a gentle simmer. Cook for 5 minutes, stirring occasionally, until the cream slightly thickens.
Reduce the 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 to taste.
Add the cooked fettuccine pasta to the skillet and toss gently to coat the pasta evenly with the Alfredo sauce.
Remove from heat and let the pasta cool to room temperature.
Transfer the pasta Alfredo to an airtight container 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 and stir gently until heated through.
Garnish with chopped fresh parsley before serving.