Melt butter in a medium saucepan and cook shallots for 1-2 minutes, stirring often. Add chopped mushrooms and cook for a minute or two. Add rice, broth, seasonings for stuffing and chopped chestnuts. Cover pot and cook for 20 minutes, or until rice is fluffy and cooked through. Remove from heat and let mixture cool for 10-15 minutes.
Place sauce ingredients in a small saucepan and simmer on high heat for 1 minute, stirring often. Reduce heat to medium-low and let sauce simmer for 3-4 more minutes, or until thickened. Remove from heat, cover and keep warm. Reserve 1/3 of sauce for serving. If it gets too thick, add 1 tablespoon of water and reheat on stove stop before using.
Preheat grill for medium high heat.
Cut a 2 inch wide by 2 1/2 inch deep pocket into the meat portion of pork chops. Fill the pockets with stuffing and secure with toothpicks; 2-3 per chop.
Place chops on grill and cook for 8 minutes, turn, baste with glaze, and cook for another 8 minutes. Repeat process until the internal temperature of the pork chops reach 165 degrees F. It is important to cook these well done since there is stuffing involved. If any flare-ups occur, move chops to a cooler part of the grill and finish cooking over indirect heat.
Once cooked through, remove chops from grill and place onto a cutting board. Let meat stand for 3-4 minutes or until the toothpicks have cooled off enough to handle. Carefully remove toothpicks and serve with warmed reserved glaze on top.