In a small saucepan, combine the sugar, 1/4 cup fresh lavender leaves (or 1 teaspoon dried lavender) and 1 1/2 cups water. Bring to a low boil over medium-high heat. Lower the heat and simmer, stirring, for 5 minutes. Let cool.
In a shaker, combine the remaining 1 teaspoon fresh or dried lavender leaves, the gin and 1 1/2 tablespoons lavender syrup (reserve the remaining syrup for another use); muddle, using a wooden spoon. Add ice cubes and shake. Strain the mixture into a champagne flute and top with prosecco. Garnish with the lavender sprig.