What exactly is the question? How to make demi glace? I don’t know anything about an appetizer at that restaurant, but I know how to make demi.
Ideally, start by making stock from bones, maybe a split hoof. Note that in a perfect world this would be veal stock, which you can make simply or use Keller’s recipe and make it perfectly, if you have 3 days. Reduce and reduce and reduce. That’s essentially it, though you’ll find some details in various recipes with aromatics and straining along the way.
The issues you are having with reducing after a braise might have to do with either too much fat content, which can interfere with the caramelization, or not enough collagen (a “braise” doesn’t tell me much about what you were braising, so not sure). You should be able to make what’s basically a demi glace post braise if you strain, defat, and reduce.
I make a very simple version in the pressure cooker, chicken carcases and wings and very well blanched pork rind, cook at full pressure with lots of vegetables and herbs just covered with water and some white wine for three hours, strain out the solids, put the liquid through a cloth which should defat as well, clean and reduce. Very little effort, 95% as good as the laborious real thing and 50 times as good as bought versions.
I don’t think that’s a reasonable comparison even though chicken in cassoulet is extremely common in SW France-if it’s the right kind and quality of chicken there’s nothing particularly wrong with it though I don’t use it myself. The point about demi-glace is that it has absolutely no specific meat flavours, just richness and texture, and if it does one is doing it wrong!.
Oh I am mostly just teasing, sorry if the humor didn’t come across. I also vocally reject the notion of a “vodka martini,” though I’d never tell a person they shouldn’t drink what they like.
I agree fully with the notion that the existence of a “vodka martini” is a mythical creation. If you want a clear flavorless alcohol shaken with ice and topped with saltwater just say so. You will note that real variations of a Martini have their own names. A Gibson or even a Manhattan come to mind. Only one requires the designation of the major alcoholic component.
Could we start a movement to rename the “vodka martini” to a Homer Simpson or maybe an Austin Powers?