Add the Granulated Sugar (1 cup) and Water (1 cup) to a small sauce pan. Bring up to a low boil, stir to dissolve sugar. Remove from heat and set the syrup aside to cool.
Muddle the Lime Juice (0.75 fluid ounce), Fresh Mint Leaves (8), and Simple Syrup (0.75 fluid ounce) by crushing in a cocktail shaker. If you don't have a muddler, you can use the handle of a wooden spoon.
Add the Rum (1.5 fluid ounce), a couple of cubes of Ice (to taste), and Angostura Bitters (2 dash). Put the lid on the cocktail shaker and shake vigorously until chilled. Strain into a coupe glass or a short rocks glass.
Top with Prosecco Wine (2 fluid ounce). Garnish with a mint leaf and serve.