Melt the butter in a small, non-stick, long-handled saucepan over medium heat. Add in the pineapple rings and cook over medium heat until both sides have darkened and the edges are starting to caramelize.
Add in the pineapple syrup and cinnamon, if using, and bring to a boil. Lower the heat, simmer and reduce the syrup until about 1/2 to 2/3's left.
Remove the saucepan from heat. Pour in the dark rum.
Method 1: Hover the saucepan over medium heat and swirl the saucepan to evenly distribute the alcohol. Tilt the saucepan forward slightly towards the flame (without spilling the sauce out) and ignite the alcohol. Swirl the saucepan gently and constantly until the flame goes out.
Method 2: Lit a really long matchstick (like satay stick). Place the flame on the surface of the sauce and the alcohol should ignite. Swirl the saucepan gently and constantly until the flame goes out. Return the saucepan over medium heat to warm up the sauce if needed.
Spoon the pineapple rings and sauce onto a serving dish. Scoop the ice cream on top of the rings and serve immediately.