Melt the butter in a large pot over medium heat. Add the onion, and garlic; saute 10 minutes.

Add the flour and stir well. Cook, stirring frequently, for 3 minutes until the flour turns golden brown

Combine the milk and half-and-half. Slowly pour into flour mixture, whisking constantly until combined.

Turn the heat up to medium-high and add the beer and mustard. Bring to a boil, whisking frequently until foam subsides.

Simmer on low heat for 10 minutes until thick. Remove from heat and whisk in the cheese a handful at a time. Taste and add salt and pepper as needed.