Trim fat from meat. Insert a meat thermometer near the center of roast. For glaze, stir together 2 tablespoons honey and orange juice.
Arrange preheated coals around a drip pan in a covered grill. Test for medium-low heat above pan. Place roast on grill over drip pan. Cover and grill for 1 to 1-1/4 hours or until thermometer registers 160 degrees F, brushing roast with glaze during the last 15 minutes of cooking. Remove roast from grill and cover with foil. Let stand for 10 minutes before slicing.
Meanwhile, for applesauce, in a medium saucepan combine apples, water, garlic, and gingerroot. Cover and bring to boiling. Reduce heat. Cover and simmer about 10 minutes or until apples are tender. Stir in 1/4 cup honey, orange peel, and cinnamon. Simmer, uncovered, for 5 minutes, stirring once or twice. Set aside. Serve roast with applesauce.