Make hole in center of brioche with a long, narrow object, and stuff with banana.

For the batter: Combine eggs, cream, and bananas in a blender and mix until smooth. Add remaining ingredients and mix well.

For the banana compote: Add all ingredients except cornstarch to a saucepan, bring to a boil and reduce heat to medium-low, and simmer until banana is barely tender, about 2 minutes. Remove from heat and stir in cornstarch mixture, return to heat and let simmer until thick and clear, about 1 more minute. Transfer to a bowl and keep warm.

For the maple butter: Combine together in a food processor until smooth.

This recipe yields ?? servings.