Cut bananas in half crosswise, and cut halves lengthwise.
Melt butter in a large nonstick skillet over medium-high heat. Add brown sugar and next 4 ingredients; cook 30 seconds. Add banana pieces, and cook 1 minute on each side.
Heat rum in a small saucepan. Pour over banana mixture. Ignite rum with a long match, if desired; let flames die down. Stir gently; top with yogurt.