Preheat oven to 450 degrees F.
Mix apple juice & cornstarch in a small bowl and set aside.
Trim the fat off lamb chops and sprinkle with salt & pepper.
Heat oil in a large ovenproof skillet over medium-high heat.
Add lamb chops to heated skillet and cook until browned on one side.
Flip lamb chops and place entire pan into the oven.
Bake lamb chops for approximately 11 minutes or when a meat thermometer in one of the lamb chops reaches 140 degrees (for medium-rare).
Transfer lamb chops to a serving platter and cover loosely with tin foil.
Place skillet back over medium-high heat on your stove-top (use a pot holder) & add shallot.
Cook shallot, stirring constantly, until browned and softened.
Add beef broth, vinegar, and mint jelly and bring to a boil. Use a fork to break up the jelly until it dissolves into the sauce.
Cook, whisking constantly, until the liquid has reduced by half.
Stir in the cornstarch mixture and bring sauce to a simmer.
Stir constantly until the sauce is thickened.
Remove sauce from heat and stir in 1 tablespoon of fresh mint.
Pour sauce over top of the lamb chops and then sprinkle another 1 tablespoon of fresh mint on top.