Red currant jelly adds a touch of sweetness to tender venison medallions.
Rub all sides of venison medallions with garlic. Brush with 1/2 teaspoon oil and season with salt and pepper.
Heat a large heavy skillet (preferably cast-iron) over high heat until very hot. Add the venison and cook until seared on all sides, 3 to 4 minutes for medium-rare; be careful not to overcook. Transfer to a plate and cover with foil to keep warm. Reduce heat to low.
Add remaining 1 1/2 teaspoons oil and shallots to the pan. Cook, stirring, until the shallots soften, about 1 minute. Add Cognac and cook, stirring, until most of the liquid has evaporated, 1 to 2 minutes. Stir in broth, jelly, mustard and thyme. Cook, whisking, until the jelly melts, 1 to 2 minutes more.
Combine cornstarch and cold water; slowly whisk into the simmering sauce until slightly thickened. Strain through a fine sieve. Discard solids. Adjust seasonings with salt and pepper.
Slice the venison and fan onto a warmed plate. Serve with the sauce.
4 lean meat, 1/2 fat