1. Pour lime juice, orgeat, orange liqueur, and rums into a glass measuring cup. Stir and chill at least 1 hour.
2. Divide rum mixture between 4 chilled Champagne flutes and top each with 1/2 cup sparkling wine. Cut 4 spirals of zest from lime (use a 1-hole bartender's zester or a sharp knife) and put a spiral in each drink along with a mint sprig.
Note: Nutritional analysis is per drink.