In a cocktail shaker, combine ice, apple cider, pumpkin puree, and pumpkin pie spice. Shake well to combine and chill.
To rim your champagne flute, add a shallow layer of brown sugar to a saucer. Dip the rim of the flute into the apple cider mixture, and then press into the brown sugar.
To serve, fill your champagne flute halfway with the apple cider mixture, strained to avoid the ice.