Cook the fettuccine pasta following the directions on the box. Drain well and rinse with cold water. Sauté the minced garlic in a skillet until fragrant. Gradually whisk in the flour, continuing to stir, creating a roux.
Slowly whisk in the heavy cream to incorporate it into the thick roux. Allow it to come to a simmer. Reduce the heat to low and stir in the cheeses. Stir until all of the cheese has melted and the sauce is creamy. Add salt and pepper to taste.
Remove the skillet from the heat. Add the cooked fettuccine noodles to the sauce and toss to coat the pasta with the alfredo sauce. If desired, sprinkle fresh parsley over the top and sprinkle with more shredded Parmesan cheese.