Preparation Using sharp knife, cut bones from pork chops. Cover and refrigerate pork. Heat 1 tablespoon oil in heavy medium skillet over medium-high heat. Add bones; sauté until brown, about 15 minutes. Pour off any accumulated fat. Add 2 cups broth to skillet. Simmer over low heat until broth is reduced to 1 cup, scraping up any browned bits on bottom of skillet, about 25 minutes. Remove bones from skillet. Add cherries and vinegar to skillet; simmer until reduced to 2/3 cup, about 8 minutes. (Can be made 1 day ahead. Cover; chill.) Sprinkle pork with salt and pepper. Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add pork; sauté until brown, about 2 minutes per side. Add remaining 1/2 cup chicken broth. Reduce heat to low. Cover and cook until pork is just firm and no longer pink in center, about 6 minutes. Transfer pork to plates. Tent with foil to keep warm. Pour cherry mixture into same skillet. Bring to boil. Reduce heat; simmer until sauce is reduced to 3/4 cup and coats back of spoon, about 5 minutes. Season with salt and pepper. Spoon over pork.
Preparation Using sharp knife, cut bones from pork chops. Cover and refrigerate pork. Heat 1 tablespoon oil in heavy medium skillet over medium-high heat. Add bones; sauté until brown, about 15 minutes. Pour off any accumulated fat. Add 2 cups broth to skillet. Simmer over low heat until broth is reduced to 1 cup, scraping up any browned bits on bottom of skillet, about 25 minutes. Remove bones from skillet. Add cherries and vinegar to skillet; simmer until reduced to 2/3 cup, about 8 minutes. (Can be made 1 day ahead. Cover; chill.) Sprinkle pork with salt and pepper. Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add pork; sauté until brown, about 2 minutes per side. Add remaining 1/2 cup chicken broth. Reduce heat to low. Cover and cook until pork is just firm and no longer pink in center, about 6 minutes. Transfer pork to plates. Tent with foil to keep warm. Pour cherry mixture into same skillet. Bring to boil. Reduce heat; simmer until sauce is reduced to 3/4 cup and coats back of spoon, about 5 minutes. Season with salt and pepper. Spoon over pork.