Heat olive oil and butter in a saucepan over medium heat. Add the chopped shallot and garlic. Cook gently for about three minutes. Stir often until they become soft and fragrant but not browned.

Stir the tomato paste into the pan. Cook it for one minute. This simple step adds extra depth and richness. It also helps create a beautiful color in the finished sauce.

Slowly add the Madeira wine. Stir well and scrape any bits from the bottom of the pan. Let the wine simmer gently. Reduce it by about half for stronger flavor.

Pour in the beef stock. Add thyme, bay leaf, and Worcestershire sauce. Stir everything together. Bring the mixture to a gentle simmer. The kitchen will start smelling amazing at this stage.

Allow the sauce to simmer for about twenty minutes. Stir occasionally. The liquid should reduce and become slightly thick. This reduction creates the rich taste that makes Madeira sauce special.

Remove the bay leaf. Pour the sauce through a fine mesh strainer. This creates a smooth texture. Return the strained sauce to the saucepan for the final step.

Add one tablespoon of cold butter. Whisk until fully melted. This makes the sauce glossy and silky. Taste and adjust with salt and pepper before serving.