Melt butter in a dutch oven (I used cast iron) a thick steel pan would work too though.
Add onions and celery and saute until softened about 4-6 min.
Stir in the flour.
Mix in the broth and milk until ingredients are well mixed (it may help to do this slowly so the flour does not lump up on you).
Add the potatoes and bring whole thing slowly to a boil.
make sure you stir occasionally so it does not stick and burn at the bottom of the pan.
Once boiling reduce heat to low and simmer with the lid only partially covering pan for about 10-15 minute.
Add the broccoli and the beer (the darker the beer you use the more pronounced the flavor will be).
cook for an additional 15-20 minute NOTE: the longer you cook at this stage the softer your vegitables will be.
cook longer if you prefer them to be soft.
Stir in the Cheese (Extra sharp cheddar is the best as it has a strong enough flavor to survive the rest of the ingrediants. Especially if you are using a dairy Aisle cheese such as kraft. in this case you must use Extra sharp.).
Stir in the Worcestershire sauce, salt, and hot pepper sauce (I prefer to add a little more hot pepper sauce to give the soup a little bit of a kick.).
NOTE: this keeps well in the refrigerator, and I would heat it up by the bowl in the microwave.
It got better each day-- However I am sure it will not keep forever so if you plan on keeping it more than a week I advise you freeze it.