Demi-glace is a thick, shiny deep brown French sauce used as a base for other sauces to give depth to complex dishes.

Demi-glace is made by boiling espagnole sauce (which is a classic French brown mother sauce made with brown stock, brown roux, mirepoix and tomato purée, cooked for several hours), skimming it and adding white stock or estouffade (clear brown stock that's used to dilute thicker brown sauces or moisten other dishes), plus Madeira or sherry and in some cases mushroom stalks until it reduces by half into a glaze-like sauce that coats the back of a spoon.

It's quite a project, and even French home cooks usually resort to dehydrated powdered demi-glace, available in supermarkets.