Step 1: Rub the bottom and sides of a heavy saucepan with the cut garlic. Add the beer and chicken stock and bring to a boil.
Step 2: Meanwhile, place the cheese and flour in a bowl and toss to mix. Sprinkle the cheese into the boiling beer mixture, stirring with a wooden spoon. Bring the sauce to a boil—it will thicken.
Step 3: Reduce the heat slightly, stir in the mustard, salt, and pepper, and gently simmer the sauce until smooth and rich tasting, 3 to 5 minutes, stirring with the wooden spoon. Keep warm until serving time, or reheat gently.
To make a lighter sauce, use an inexpensive lager style beer of the sort mass-marketed in cans. To make a darker, richer sauce with a pleasantly bitter edge, use a dark beer.