1. Place pineapple juice in a heavy saucepan over high heat; bring to a boil, and cook until reduced by half (3-5 minutes).
2. Remove pan from heat and add rum. Return to heat, add sugar, butter, and cinnamon to juice mixture; boil 3-5 minutes or until thick, stirring well with a whisk. Remove from heat, and set aside.
3. Using a metal skewer, make a starter hole in the center of each plum quarter (from skin side to pit side). Skewer 2 plum quarters on each cinnamon stick, facing the same way, placing a strip of lemon rind between each plum quarter. (The recipe can be prepared several hours in advance up to this point.)
4. Set up your grill for direct grilling, and preheat grill to high. Clean and oil grate.
5. Arrange the plum kebabs on grate, and grill 3-5 minutes per side or until sizzling and golden, basting lightly with pineapple-rum sauce.
6. When the kebabs are nearly done, scoop the ice cream or frozen yogurt into glasses. Top each portion with a plum kebab; drizzle with remaining sauce, and garnish with grated lemon rind. Serve immediately.