Melt the butter in a large skillet over medium heat. Add the brown sugar and cinnamon and cook, stirring, until the sugar dissolves, about 2 minutes. Add the pineapple rings and turning, cook on both sides until the rings start to soften and brown, about 3 minutes. Carefully add the rum and shake the pan back and forth to warm the rum and flame the liquid. (Or, off the heat, carefully ignite the liquid with a long kitchen match and return to the heat when the flames die down.) Shake the pan back and forth, basting the rings, until well coated with the sauce.

Divide the ice cream among 4 dessert plates. Gently lift the pineapple rings from the pan and place 4 pieces on each scoop of ice cream. Spoon the sauce over the ice cream and rings, and serve immediately.

Combine the cream, milk, sugar, vanilla bean and seeds in a medium heavy saucepan and bring to a gentle boil over medium heat. Remove from the heat.

Beat the egg yolks in a medium bowl until frothy and lemon colored, about 2 minutes. Whisk 1 cup of the hot cream into the egg yolks in a slow, steady stream. Gradually add the egg mixture to the hot cream, whisking constantly. Cook over medium-low heat, stirring occasionally, until the mixture thickens enough to coat the back of a spoon, about 5 minutes.

Remove from the heat and strain through a fine mesh strainer into a clean bowl. Cover with plastic wrap, pressing it directly against the surface of the mixture to keep a skin from forming. Refrigerate until well chilled, about 2 hours.

Pour the mixture into an ice cream maker and freeze according to the manufacturer's instructions. Transfer to an airtight container and freeze until ready to serve.

Yield: 1 quart