Mix simple syrup and lime juice in a cocktail shaker. Muddle the mint leaves gently with a wooden spoon or muddler (bruise the leaves, so the flavor seeps out).
Add rum and bitters, then fill the rest of the shaker with ice.
Shake until the mixture is thoroughly chilled.
Pour through a double strainer (to avoid bits of mint leaves) into a chilled cocktail glass.
Top with champagne and garnish.
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