To make the syrup, heat the sugar and water in a small saucepan over medium heat. Stir until the sugar has dissolved.
Add in the cinnamon, ginger, lime zest, vanilla bean, and chopped rhubarb. Bring to a boil then reduce heat to a simmer. Simmer for 10 minutes. Remove from heat and stir in the rum.
Cool the syrup completely. It can be stored in the refrigerator for up to 1 week.
To make the cocktail, spoon one ounce of the rhubarb syrup into a champagne glass, making sure to get a few pieces of the chopped rhubarb. Fill the glass with chilled champagne. Place a thin slice of rhubarb in the glass and enjoy.