Make caramel: Stir sugar and 1/2 cup water in a pan over medium-low heat until sugar dissolves. Raise heat to medium-high. Watching carefully, boil syrup without stirring until it is a dark amber color, 10 to 15 minutes. Remove from heat and carefully pour in cream (mixture will bubble up and splatter). Reduce heat to low; cook, stirring constantly, until mixture thickens and becomes smooth, 2 to 5 minutes. Remove from heat; whisk in butter, vanilla and salt.
In a bowl, mix brown sugar and cinnamon. Warm honey in microwave for 15 seconds.
Preheat grill to medium-high. Cut unpeeled bananas in half lengthwise. Brush cut sides with honey; sprinkle with sugar mixture. Oil grill. Place bananas on grill, cut sides up. Cook until bananas are tender and flesh pulls away from skin, 3 to 4 minutes.
Using 2 spoons, gently remove 2 banana halves from peels. Place 2 halves in a bowl, top with ice cream and drizzle with caramel. Repeat with remaining bananas, ice cream and caramel.