Melt the butter over medium heat in a medium saucepan. Add the garlic and saute for about 1 minute. Whisk in the flour and stir for 1 minute.
Slowly whisk in the half and half. Turn heat to medium-high and whisk occasionally until the mixture comes to a slow boil. Reduce heat to simmer and stir in the cheese; stir until melted. Add salt only if you have used unsalted butter. Add about 1 tablespoon fresh chopped parsley, if desired.
Use Alfredo sauce immediately for your recipe, or refrigerate (covered) until ready to serve. Sauce will stay nicely in the refrigerator for about 1 week.