Finely chop the fresh rosemary.
Lightly crush the whole peppercorns using a mortar and pestle or the back of a spoon.
Mince the shallot finely.
In a medium saucepan, melt the butter over medium heat.
Add the minced shallot and sauté until softened and translucent, about 2-3 minutes.
Add the chopped rosemary and crushed peppercorns to the saucepan. Sauté for another 1-2 minutes, until fragrant.
Add the red wine into the pan to deglaze, scraping up any browned bits from the bottom. Allow the wine to reduce by half, about 3-4 minutes.
Pour in the demi-glace, stirring to combine with the aromatics and reduced wine. Bring the mixture to a gentle simmer over medium-low heat.
Stir in the Dijon mustard, blending it well into the sauce.
Let the sauce simmer gently, allowing it to reduce and thicken slightly. This should take about 5-10 minutes. Stir occasionally to prevent sticking and ensure even cooking.
Taste the sauce and season with salt if needed.
Strain the sauce through a fine-mesh sieve to remove the solids for a smooth texture. Optional
The rosemary peppercorn sauce is now ready to be served. Drizzle it over your favorite meats, such as steak, lamb, or pork.