Demi-Glace

Melt about a third of the clarified butter in a heavy-bottomed pot over medium heat. Add the mirepoix and cook, stirring occasionally, until the onions have gone past translucent and the whole mixture is deeply browned and sweet-smelling — 12 to 18 minutes. Let the sugars in the carrot and onion caramelize against the pan; the fond that builds on the bottom is the start of everything.

With the remaining clarified butter melted in the cleared part of the pot, sprinkle in the flour and stir it into a paste. Cook the roux slowly, stirring almost constantly, watching it move through blond to peanut-butter and on toward a deep chestnut brown. This can take 10 to 20 minutes. It will smell increasingly nutty and toasty — like baking pie crust. Go low and patient; a brown roux is one careless minute from burnt.

Stir the tomato paste into the roux and mirepoix and cook it out for 3 to 5 minutes — the pinçage. Keep it moving over medium heat until the paste loses its raw, bright-red look, darkens to a brick-rust color, and smells sweet and concentrated rather than sharp and tinny. Cooking the tomato now removes its raw acidity and builds another layer of caramelized depth.

Pour in the first measure of brown stock a few ladles at a time, whisking hard after each addition to work out lumps before adding more. Once it is smooth, drop in the bouquet garni and bring it to a bare simmer, whisking as it thickens so the roux does not catch and scorch on the bottom.

Hold the sauce at the barest simmer for 2 to 3 hours, stirring now and then and skimming the fat and grey froth from the surface, nudging the pot half off the burner so impurities gather on one side. Season lightly with salt — remember it will concentrate further. When it has reduced by roughly a third and coats a spoon, strain out the solids and bouquet garni through a fine sieve. This is your base espagnole.

Combine the strained espagnole with an equal volume of fresh brown stock in a clean wide pot. Bring to a gentle simmer and reduce by half, skimming patiently and constantly as fat and impurities rise — this is what gives demi-glace its clarity and shine. Take your time over low heat; an aggressive boil will cloud and muddy it. The sauce is ready when it has reduced by half, turned glossy and syrupy, and coats the back of a spoon in a clinging, lacquered nappe.