Prepare mint simple syrup. In an old-fashioned style glass, add blueberries and about ½ ounce of mint syrup. Muddle (smash) the blueberries against the bottom of the glass until crushed. Add ice, limon rum, and lime juice. Stir well. If needed, sweeten with additional mint syrup to taste.
Fresh Mint Simple Syrup
Combine sugar, water, and mint in a small sauce pot. Bring to a boil, reduce heat to a simmer and cook just until sugar is completely dissolved. Remove from heat and cool before using.