Gather the ingredients.

Place the bay leaf, thyme, parsley stems, and peppercorns on a square of cheesecloth.

Tie it up into a bundle with cooking twine to create the sachet d'épices.

In a heavy-bottomed pot over medium heat, heat the butter and add the chopped onions, celery, and carrots. Sauté for a couple of minutes, until the onions are partially translucent.

Sprinkle in the flour and stir to form a paste. Cook for about 3 minutes, stirring frequently until the flour is lightly browned, but by no means burned.

Whisk in 3 cups of the beef stock.

Bring to a boil over medium-high heat. Then lower the heat to a simmer , add the sachet, and reduce for about 20 minutes, or until the total volume has reduced by about a third.

Remove the pan from the heat and retrieve the sachet (set it aside). Carefully pour the sauce through a wire mesh strainer lined with a piece of cheesecloth and use a spoon to gently push the sauce from the remnants of the mirepoix (the sautéed vegetables).

Return the sauce to the pan, stir in the remaining 2 cups of stock, and return the sachet to the pot.

Bring the pot back to a boil and then lower the heat to a simmer. Simmer for about 50 minutes or until the sauce has reduced by half.

Discard the sachet. Strain the sauce through a fresh piece of cheesecloth.

If using the demi-glace as is for a dish, season to taste with kosher salt. When adding it to another sauce recipe, wait to season that sauce until the very end.