Place the shredded cheese in a bowl and add 2 tablespoons flour. Toss to coat the cheese thoroughly.
In a saucepan over medium heat, melt the butter. Add the garlic and stir until nutty, about 15 seconds. Add in the last tablespoon of flour and whisk to combine. Once the flour has browned a bit, add in the milk and whisk to combine. Let the mixture to come to a simmer, whisking the entire time.
Once the mixture is thickened a bit, add the shredded cheese, a handful at a time, making sure each addition is completely melted before adding the next. Keep warm and stir until completely smooth.
Transfer to a fondue pot to keep warm while you enjoy the dipping.