Adding ice cream to the caramel sauce makes it extra rich and especially silky.
Heat sugar in a large heavy-bottomed saute pan over medium-high heat. Let stand until edge of sugar starts to melt and turn golden. Carefully swirl pan to incorporate all of the sugar. Continue cooking until sugar is a golden-brown caramel, 6 to 8 minutes.
Reduce heat to low, and stir in butter. Add bananas, carefully roll in caramel, and cook, turning bananas occasionally until just soft, 3 to 5 minutes. Remove bananas from caramel, and place in serving dishes. Add 1/2 cup of vanilla ice cream to caramel sauce, and stir until smooth and creamy. Scoop remaining ice cream over bananas, pour caramel over ice cream, and sprinkle with chocolate shavings.