1. Slice pineapple crosswise into 1/2-inch-thick rings. With a small, sharp knife, cut out the core from each slice. Set the rings aside. (Can be prepared a day ahead. Wrap well and refrigerate.)
2. In a small saucepan, melt butter over medium-low heat. Add brown sugar, orange juice, and cinnamon, stirring constantly with a wire whisk until sugar is melted and sauce begins to bubble. Remove from heat. Let sauce cool to room temperature before serving.
3. Heat grill. Grill pineapple rings 3 to 5 minutes per side, until edges are browned. To serve, divide pineapple rings among four bowls, pour brown sugar sauce over pineapple and scoop coconut sorbet over top. Sprinkle with toasted coconut and crystallized ginger, if desired. Makes 4 servings.