How to Make It
Using a larding needle, thread the vanilla bean quarters crosswise through the pineapple. Remove the spit from the rotisserie attachment and heat the grill. Skewer the pineapple on the spit, pushing it to the center. Reattach the spit to the motor. Cook the pineapple, brushing occasionally with olive oil, until slightly softened, about 1 hour.
Meanwhile, in a medium saucepan, melt the butter over moderate heat. Add the sugar and cook, stirring, until dissolved, then cook, undisturbed, until light brown. Carefully swirl the pan and cook until the caramel turns deep amber. Carefully add the bananas, ginger and 1 cup of water; the hot caramel will sputter. Stir until the caramel melts. Add the jalapeño and vanilla seeds and cook, stirring occasionally, for 5 minutes. Scrape the mixture into a blender and puree until smooth. Add water, 1 tablespoon at a time, if needed to loosen. Let cool completely.
Transfer the pineapple to a carving board and let it cool slightly. Cut as desired. Serve with the caramel sauce and ice cream.