Step 1 Heat a small, heavy-bottom saucepan over medium-high heat. Add the oil, then the carrot, onion, leek, shallot, garlic and peppercorns and saute until the vegetables are tender, 3 to 5 minutes, stirring occasionally. Stir in the thyme and bay leaf and cook for 30 seconds.
Step 2 Stir in the Cognac and red wine. Bring to a boil and cook until reduced by one-third, about 3 minutes.
Step 3Add the vinegar and broth and bring to a boil over high heat, then reduce the heat and simmer until reduced by one-third, about 30 minutes.
Step 4Strain the sauce through a fine-mesh strainer set over a bowl and discard the solids. Season to taste with salt and pepper and keep covered in a warm place until needed.