Sauce – Why do sauces thicken as they cool

The simple answer is: You reduce a cream sauce the same way you reduce any other sauce, by simmering it until a certain amount of liquid is gone, just like the instructions said. You have to be careful about temperature though, because milk (or cream) can burn at high temperatures, and then your sauce is ruined. You should keep it to a low or at most medium simmer.

Cream sauces normally tend to thicken extremely fast, so the long cooking time is almost certainly due to watering it down. I don't think the water was necessary at all; the chicken broth was probably for flavouring, and although "broth" is a somewhat nebulous term, one would normally expect a broth to contain at least some amount of gelatin, which will cause the sauce to thicken substantially when it cools if you reduce it a lot. Water doesn't, so you've added no flavour and thinned out the sauce.

Basically, you (or your wife) added water for no other purpose than to try to evaporate it later. Water generally doesn't go in a cream sauce. If you don't have chicken broth or can't use it, I would either substitute more wine or just leave it out completely. Usually the only time you substitute water for broth is if it's actually the base of your sauce.

Major ways of thickening a sauce -- or, for that matter, some other liquid:

• Starch (e.g., flour, cornstarch, tapioca, arrowroot)
• Emulsion (e.g., butter, cream, yolk, mustard, blending in lecithin-and-fat)
• Coagulated protein (e.g., blood, egg, pureed seafood)
• Gels/polysaccharides (gelatin, alginate, xanthan, pectin, agar agar, guar gum)
• Suspension (general puree of solids)

Note that some of the examples of one category can also fit into another.