Heat oven to 325°F. Place ham, fat side up, in shallow roasting pan. If necessary, trim fat from ham. Score ham diagonally at 1-inch intervals, cutting about 1/4 inch deep; score in opposite direction to form diamond shapes. Insert meat thermometer so bulb reaches center of thickest part of ham but does not rest in fat or on bone. Bake at 325°F. for 1 hour.
Meanwhile, in small saucepan, combine all remaining ingredients; cook over medium-low heat for about 5 minutes, stirring occasionally. Reserve about half of preserves mixture to serve with ham.
Remove ham from oven. Remove pan drippings from pan. Brush or spoon some of remaining preserves mixture over ham. Return to oven; bake an additional 1 to 1 1/2 hours or until meat thermometer registers 140°F., brushing or spooning preserves mixture frequently over ham.
Remove ham from oven. Cover with foil; let stand 5 to 10 minutes before slicing.
Meanwhile, return reserved preserves mixture to small saucepan; heat over low heat for 2 to 3 minutes, stirring occasionally. Serve ham with preserves mixture. If desired, garnish with sliced green onions.