Preheat oven to 375 degree F. Season lamb generously with salt and pepper. In a very large skillet brown lamb on all sides in hot oil. Set skillet aside. Place lamb, bone-side down, in a foil-lined, shallow roasting pan.
In a small bowl combine jam, mustard, and 1 teaspoon of the garlic; spoon over lamb. Sprinkle evenly with crumbs. Roast, uncovered, for 35 to 40 minutes for smaller roasts or 50 to 60 minutes for larger roast until thermometer inserted in thickest portion registers 140 degree F (medium-rare) to 155 degree F (medium). Transfer to serving platter. Cover with foil and let stand 10 minutes before slicing (meat temperature will rise 5 degree F during standing).
Meanwhile, in the large skillet cook raspberries and remaining garlic for 30 seconds. Add beef broth; heat to boiling. Boil gently, uncovered, for 5 to 8 minutes or until reduced to 2/3 cup. Cool slightly; transfer to a blender. Cover and blend until almost smooth. Stir in mint. Season to taste with salt and pepper. To serve, slice lamb between ribs and spoon sauce over lamb. Makes 8 servings.