In a small bowl, soak 8 wooden picks in water for 10 minutes.
Meanwhile for stuffing, in a saucepan, cook mushrooms and onion in hot butter until onion is tender. Remove from heat. Stir in grated ginger, the 1/4 teaspoon salt, and the 1/4 teaspoon pepper. Add spinach and bread crumbs, tossing gently to combine.
Make a pocket in each chop by cutting horizontally from the outside edge almost to the bone. Divide stuffing evenly among pockets in chops. Secure openings with water-soaked wooden picks. Sprinkle chops with salt and pepper.
To bake stuffed chops, after stuffing and sprinkling chops with salt and pepper, brown in a small amount of oil in a large skillet. Transfer to a baking dish. Bake, uncovered, in a 375°F oven for 35 to 45 minutes or until juices run clear (160°F), brushing with ginger preserves during the last 5 minutes of baking.
Meanwhile, trim roots and tops of the green onions. In a medium skillet, cook green onions in hot oil for 1 to 3 minutes or until slightly softened. Serve green onions with the chops.
In a grill with a cover arrange medium-hot coals around a drip pan. Test for medium heat above pan. Place chops on grill rack over pan. Cover and grill for 35 to 40 minutes or until juices run clear (160 degree F), turning once and brushing occasionally with ginger preserves during the last 5 minutes of grilling. Remove wooden picks before serving.