Melt butter in a 10-inch heavy skillet over moderately high heat until foam subsides, then saute banana, cut sides down, shaking skillet, 1 minute. Remove skillet from heat (away from flame) and sprinkle brown sugar around banana, then pour rum around banana. Return skillet to heat and continue to saute, shaking skillet occasionally, until sugar begins to melt, about 30 seconds. Add water, nutmeg, cinnamon, and a pinch of salt and cook over moderate heat, shaking skillet occasionally, until sauce is slightly thickened, 1 to 2 minutes. Serve banana hot, sprinkled with nuts.