Spray both sides of the pineapple rings with nonstick cooking spray. Rub the pineapple slices with the dark brown sugar.
In a small chilled bowl, beat the cold whipping cream with an electric beater until it starts to thicken. Add the confectioners' sugar and beat until it forms soft peaks. Add the rum and continue beating until medium stiff peaks form.
Heat a grill or grill pan until very hot. Spray the grill with more nonstick cooking spray. Brush the pineapple slices with butter and lay the pineapple in a single layer on the grill until browned, turning once, 1 to 2 minutes per side.
Add the pineapple and let roast until brown. Remove to a plate and allow to cool slightly.
Arrange the pineapple slices on a serving platter, then add a large dollop of the chilled whipped cream to each slice. Serve 2 pineapple rings per person. Garnish; with small bunches of mint or a few mint leaves.