• Combine the rum, lime juice, and blueberry syrup in a shaker filled with ice.
• Shake vigorously for 10-15 seconds, or until the shaker feels very cold.
• Strain the cocktail into a chilled coupe glass.

To make the blueberry syrup

• Combine the blueberries, sugar, and water in a small saucepan. Bring to a boil over medium-high heat, until the sugar has dissolved and the blueberries have burst.
• Reduce the heat to low and simmer the mixture for 10-15 minutes.
• Strain the syrup through a fine-mesh sieve into a bowl or jar, pressing down on the solids to extract as much liquid as possible.
• Let the syrup cool to room temperature.