In a small bowl, mix 1/2 teaspoon of rosemary, pepper, salt, oregano, sage, and garlic, stir well. Rub evenly on both sides of lamb chops and place on a plate. Cover meat and refrigerate for 1 to 2 hours.
In a small pot, mix the vinegar, beef broth, sugar and remaining 1 teaspoon of rosemary. Cook over low heat, bring to a boil, continue cooking for 1 additional minute, remove from heat, and let cool. Strain through a mesh strainer and save liquid.
Preheat broiler. Spray nonstick cooking spray onto the rack of a broiler pan. Broil lamb chops 5 1/2 inches away from heat until done, about 8 minutes per side.