1. Combine first 5 ingredients in a small saucepan; bring to a boil. Cook until reduced to 3 tablespoons (about 10 minutes). Strain mixture through a sieve over a bowl; discard solids. Add butter, stirring constantly until smooth. Stir in salt and pepper.
If you make homemade demi-glace, freeze the leftovers in ice cube trays, and use it to enrich sauces or stews.