The regional table / Wisconsin
Beer Cheese Soup
Every failure of this soup is a temperature failure, and the two temperatures are the one you melt the cheese at and the one you add the beer at.
The oldest printed beer cheese soup anyone can currently reach in an open archive is not from Wisconsin, and it already knew the rule. Georgia Historic Newspapers — open to scripts where the Library of Congress is not — returns nine hits for the exact phrase, and the earliest is the Wheeler County Eagle of Alamo, Georgia, for 23 November 1962, running a syndicated food column headed "Beautiful Beer Cheese Soup!" and dated to the cheese trade's own calendar: "In honor of October, which is Cheese Festival Month". The recipe under it is butter, diced celery, carrot and onion softened without browning, six tablespoons of flour and a quarter teaspoon of dry mustard blended in, six cups of chicken broth stirred in gradually "until slightly thickened", Tabasco, a cup and a half of grated Cheddar heated "until cheese is melted", and then, in its own sentence, "Just before serving, add beer; heat to serving temperature." Twelve ounces of beer or ale, eight servings, garnish with parsley or croutons. Sixty-four years later that is still the correct architecture and still the correct order.
What makes it a Wisconsin dish is the cheese, and the scale of that is on the record too. Lee Jay Schenkenberg's 1916 master's thesis at the University of Wisconsin, "The Relation of Moisture to Quality in Wisconsin Cheddar Cheese", opens by citing the 1910 Census: Wisconsin produced 147,907,910 pounds of cheese, which was "46% or approximately one-half of the production of the whole nation, and half again as much as New York, her nearest competitor". Twenty years earlier the state had been behind New York with 21.3 per cent of the national output. The thesis then does the unglamorous work the state built its reputation on — analysing samples graded by the dealers who sold them, and finding that thirty-three export cheeses averaged 37.08 per cent moisture, sixty-nine "good" cheeses 38.59, and eighty-five called too moist 41.45, from which it concluded that 40 per cent moisture is too high for good cheese. The federal standard of identity for cheddar, 21 CFR 133.113, now fixes the maximum moisture at 39 per cent by weight and the minimum milkfat at 50 per cent by weight of the solids. Half fat, under two-fifths water: that is what you are melting, and it is why it behaves the way it does.
Why this version works
The roux is the emulsifier. Cheese is fat suspended in a protein net, and heat makes the net contract and squeeze the fat out. Industry solves this chemically: 21 CFR 133.169 lets pasteurized process cheese carry sodium citrate or a phosphate salt "in such quantity that the weight of the solids of such emulsifying agent is not more than 3 percent of the weight of the pasteurized process cheese". A home kitchen has no citrate, so starch does the job instead — gelatinised flour thickens the water phase enough that the fat droplets cannot find each other and coalesce. Skip the roux and you get oil on top, every time.
Brewers proved it with hardware. The same handbook describes a "Hop Aroma or Hop Oil Condenser" bolted to the brewing kettle's ventilator: a damper closes, cold water runs through a nest of tubes, "the volatilized hop oil is condensed around the tubes, and flows into a collecting receptacle", and the recovered oil is added back to the wort in the fermenting tub. Men whose living depended on hop aroma built a machine to catch it escaping from a boil. That is the whole argument for adding your beer off the boil, made by people with money at stake.
The cheese goes in off the heat. The same regulation tells you where the danger line sits: process cheese is heated "for not less than 30 seconds at a temperature of not less than 150 °F", which is enough to melt it and is also about where unprotected casein starts knitting into strings. Take the pot off the burner, let it stop bubbling, and add the cheese in handfuls. The residual heat of four cups of thickened broth melts a pound of cheddar without any flame under it.
The beer goes in last, and here is why. Hop bitterness and hop aroma are two different substances with two different boiling behaviours. Wahl and Henius's American Handy-Book of the Brewing, Malting and Auxiliary Trades of 1901 puts it plainly: "'Hop-Balsam' or lupulin consists of the volatile oil of hops and hop-rosin. The oil gives to the beer aroma and flavor, the hop-rosin imparts the bitter taste and helps preserve the beer." The aroma is volatile and leaves with the steam; the bitter resin is not and stays behind, concentrating as the liquid reduces. Boil the beer into the soup and you have deliberately thrown away the half you wanted.