How to reduce a sauce at the bottom of a baking dish

Your question makes me think of demi-glace. From your question, I would say that you're trying to get a nice shiny thick sauce for your duck, one that tastes of red wine.

If that's your goal, I would recommend you

1. Reduce your stock down until it's about the total volume of liquid that you're going to want. The stock reduction should be roughly the consistency you want your final sauce to be.

2. Add an equal volume of wine

3. Reduce down to desired consistency (so about by half).

This will give you a lovely sauce, with lots of that sticky goodness that reduced stocks deliver so nicely.

You might do this with all of your stock, then freeze cubes of unused sauce for later; they make a great addition to other bases.

Left-over alcohol is not going to be an issue here, by the way, you'll have long since boiled/simmered it off.

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.