Coarsely chop 1 small onion (3 ounces/100 grams) and half a medium carrot (3 ounces/100 grams); you can also strain out the vegetables from the marinade and use those. Brown the vegetables in 1½ ounces (45 grams) butter with 1 pound (500 grams) trimmings from red meat or game. As the meat begins to brown, add 3 sprigs of fresh thyme, half a bay leaf, and 1 small handful of parsley stems. Cook the mixture for several minutes more. When the vegetables and meat trimmings are well browned, tilt the pan and drain off the butter.
Moisten the browned trimmings and vegetables with 5 fluid ounces (150 milliliters) white wine vinegar and 6 tablespoons (90 milliliters) white wine. Reduce the liquids until they evaporate completely, leaving a caramelized glaze on the bottom of the pan.
Add 2 cups (500 milliliters) demi-glace or concentrated brown stock (four to six times), 1 quart (1 liter) brown game, beef, or chicken stock, and 2 cups (500 milliliters) of the strained marinade or white wine. Bring the liquids slowly to a simmer and skim off any froth or scum that floats to the top. Reduce by half. Cover the pot and cook over a very low flame for 3 hours.
Skim off any fat or scum that has floated to the top of the sauce during simmering. Crush 10 whole peppercorns and add them to the hot sauce. Let them infuse for 10 minutes and then strain the mixture through a fine chinois into a fresh saucepan.
Add ½ cup (125 milliliters) strained marinade and ½ cup (125 milliliters) brown beef, game, or chicken stock to the strained sauce. Gently bring the sauce back to a simmer. Skim the sauce and reduce it until it has a lightly syrupy consistency. Strain through a fine chinois and finish with 2 ounces (60 grams) butter.