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1
Bring the demi-glace to a gentle simmer in a saucepan over medium heat. It should tremble at the surface without rolling; a vigorous boil drives off the gelatin structure before the wine is added.
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2
Add the Madeira. Maintain a gentle simmer for 10 minutes. The sauce reduces by approximately one-fifth. This is where the dish lives or dies: the demi-glace must be gelatin-rich and of full espagnole depth before the wine enters — the Madeira only highlights what is already there. At the end of 10 minutes, the raw alcohol bite is gone and the flavours have married; taste to confirm the Madeira is a note, not the melody.
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3
Remove the pan from the heat. Mount the sauce by whisking in the cold butter piece by piece until fully incorporated. The surface becomes glossy and the wine's edges round. Do not return to the boil.
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4
Pass through a fine chinois into a warm vessel. The finished sauce is deep brown with a reddish tinge, glossy, and carries the aroma of roasted meat enriched with a nutty, slightly caramelised wine presence.