Halve garlic cloves and rub the cut sides on the inside of a 3-quart saucepan. Discard garlic. Add butter and melt over low heat. Add chopped green and red peppers and cook 2 minutes. Add flour and cook, stirring constantly, 2 minutes. Increase heat to medium-high and add Brut. Bring to a boil and cook, stirring constantly, 2 to 3 minutes.

Reduce heat to low and add cheese, a handful at a time, stirring in between additions. Stir until mixture is thick and smooth. Serve immediately with fresh bread or pretzels.