Muddle mint leaves and demerara syrup in a chilled Collins glass. Add rhum, lime, and pebble ice, then swizzle and top with more pebble ice. Add 2 dashes Peychaud's Bitters and 2 dashes Angostura Bitters. Garnish with a mint sprig.
Swizzles are traditionally prepared with a barspoon-length dried branch from a tropical bush that has five pruned prongs at the end. —Jules Bergeron, Trader Vic's Bartender's Guide, 1947