In a medium saucepan, over medium heat, add butter. Once melted, add minced garlic cloves and saute 1-2 minutes. Whisk in arrowroot (or cornstarch) until a roux is formed (texture will be pasty).
Pour in 12 oz beer, and half of cheese; whisk together.
Slowly add in remaining cheese, and mix well until smooth, and melty.
Serve immediately, or transfer to a mini crockpot to keep warm during a party.