Melt butter on low heat. Once melted, add flour and whisk smooth. Increase heat very slightly, observing and occasionally whisking while roux bubbles. Observe the initial smell, this is raw flour. Whisk occasionally and continue to smell until the scent of raw flour disappears. The importance of this step is that you want to cook the flour, but not brown it.
At this stage, you have 2 choices:
1. Simmer the sauce with the additional 1/3 c water for 20 minutes to fully thicken sauce and cook away alcohol from beer,.
2. Simmer the sauce for 5 minutes with 1 Tbsp water,.
At the end of previous step, add Worcestershire sauce and Dijon mustard, whisk inches.
With heat on low/low-medium, begin whisking in cheese, at most 1/2 c at a time. Whisk until blended after each addition, then whisk occasionally until each batch is melted.
When all cheese is melted in, dip is ready.
Ideally, serve from small warming crockpot or fondue pot, or serve immediately in warm bowl or individual rammekins.