1) Quarter apples and place entire apple (seeds and core included) in large saucepan with the 1 bunch mint, water, vinegar and jalapeno. Bring to a boil then lower to a simmer and cook until apples are tender, 15 to 20 minutes. Mash and pour into a cheesecloth-lined sieve over a bowl. Let sit to drain until you have about 2 cups of juice. Do not squeeze the apple mixture in the cheesecloth to extract more juice. Pour the stained juice into the saucepan and stir in the sugar. Bring to a boil, lower the heat to a simmer and cook until reduced by half and becomes thick. Reserve half the jelly for serving and half for brushing on the chops as they grill. Let jelly cool slightly before brushing the chops.
2) Preheat grill to medium-high heat.
3) Season lamb chops with salt and pepper and lightly coat with oil. Grill on each side for about 3 minutes, for medium rare, continuously brushing with the glaze. Mix the remaining 1/4 cup of chopped mint into reserved jelly and serve alongside grilled chops.