Heat a grill to medium-high. Brush the grates lightly with canola oil.
Whisk brown sugar, honey, melted butter, lime juice, cinnamon, vanilla, and salt in a bowl. Stir in rum if using.
Pat the pineapple dry. Brush lightly with some of the glaze on both sides.
Grill pineapple 2–3 minutes per side until charred and caramelized. Brush with more glaze as it cooks.
Transfer to a platter. Drizzle any remaining glaze over the fruit.
Top with toasted coconut and mint. Serve warm with scoops of vanilla ice cream.