Preheat a grill to high, and lightly oil the grill grate.

Place the banana halves, cut side up, on a baking sheet and drizzle the honey evenly over them. Sprinkle with the brown sugar. Place the bananas, cut side up, directly on the grill, arranging them so they are perpendicular to the grill grate. Close the grill cover and cook until the bananas are caramelized around the edges and the fruit is beginning to pull away from the peel, 3 to 5 minutes.

Carefully transfer the grilled banana halves (still in their skins) to a small baking sheet. Using two small forks or a long, thin spatula, carefully remove the banana halves from their skins and place 2 pieces of banana on each dessert plate. (This is a little tricky because the bananas are now very soft.) Top each banana with 1 or 2 scoops of vanilla ice cream. Drizzle with the Hot Fudge Sauce and Rum Caramel Sauce. Top with dollops of whipped cream and sprinkle with chopped peanuts. Garnish each banana split with a maraschino cherry, and serve immediately.