Coconut caramel version #1: Make the coconut-caramel sauce. Combine the palm sugar and coconut milk in a heavy saucepan. Bring to a boil over medium heat, whisking to dissolve the sugar. Briskly simmer the mixture until thick, golden, and very flavorful, about 5 minutes, whisking often. Remove the pan from the heat and let the mixture cool to room temperature. Place the sauce in a deep bowl. The caramel sauce can be prepared ahead.

Coconut caramel version #2: Place the sugar in a heavy pan over medium-high heat. Cook until the sugar melts, turns golden brown, becomes very fragrant, and starts to smoke, 3 to 5 minutes. Swirl the pan so the sugar cooks evenly, but do not stir. Don’t let it burn. As soon as the sugar browns, remove the pan from heat and add the coconut milk. Stand back-the mixture will hiss and sputter like Mount Vesuvius. Return the mixture to the heat and simmer, whisking until the sugar is completely dissolved. Let cool to room temperature. Place the sauce in a deep bowl. The caramel sauce can be prepared ahead.

To finish grilling the bananas: Set up your grill for direct grilling and preheat to high. Brush and oil the grill grate.