Trim fat from meat. Using sharp knife, cut slits in the meat at 1-inch intervals. Insert garlic slices into the slits. Brush the meat with 1 tablespoon oil; sprinkle lightly with salt and ground pepper.
Cook the meat in large skillet over medium heat until done, turning once. (For venison, allow 10 to 12 minutes for medium doneness; for pork, allow 20 to 25 minutes or until juices run clear (160°F.)
Meanwhile, for sauce, cook shallot and garlic in the remaining tablespoon hot oil in a medium saucepan, for 2 to 3 minutes or until tender. Stir in blackberry preserves and broth. Bring to boiling; reduce heat. Simmer, uncovered, for 4 to 6 minutes or until reduced to about ⅓ cup, stirring often. Stir in butter and honey.
Slice the meat; arrange on serving platter. Spoon the sauce over the meat.