Remove the top, bottom, and peel from the pineapple.
Slice the pineapple into 1/2- to 3/4-inch-thick rings and remove the center core.
Pat the pineapple rings dry.
Combine the melted butter, dark brown sugar, cinnamon, and salt in a small bowl.
Stir in the optional dark rum away from any open flame.
Brush both sides of the pineapple rings with the brown sugar mixture.
Preheat the grill to direct medium heat, about 375–400°F (190–205°C).
Place the pineapple rings on the hot grill.
Grill for 2–3 minutes, then turn.
Grill the second side for another 2–3 minutes, until caramelized and lightly marked.
Remove from the grill and serve warm.
If desired, serve two pineapple rings with a scoop of vanilla ice cream.