Cut a thin slice from the bottom and top of each onion, leaving onion skins on. Scoop out onion centers, leaving about 1/4-inch-thick shells. Finely chop enough of the removed onion centers to measure 1/3 cup. Brush onions with oil. For filling, in large skillet cook the 1/3 cup reserved onion centers, mushrooms, carrot, and pepper in 1 tablespoon of the margarine for 5 minutes. Slowly add the 1/2 cup cider. Stir in apple, rice, nuts, and salt; cook for 1 minute more. Remove from heat. Stir in 1/2 cup of the bread crumbs and basil. Spoon filling into each onion shell.
Arrange stuffed onions in a 2-quart rectangular baking dish. Pour the 1/3 cup apple cider around stuffed onions. Bake, covered, in 350 degree F oven about 40 minutes or until onions are tender. Melt remaining margarine and stir together with remaining bread crumbs; sprinkle over onions. Bake, uncovered, for 5 to 15 minutes more or until onions are tender. Remove outer skins before eating. Makes 6 side-dish servings.
Large, round onions work best for stuffing. Apple in the stuffing add sweetness; rice adds nuttiness too.