Make the simple syrup.  In a small saucepan, combine the sugar and water.  Bring to a boil, stirring constantly to dissolve the sugar.   Once it comes to a boil and the sugar is fully dissolved, remove the pan from the heat.  Crush 4 mint leaves between your fingers to release their oils and put them into the simple syrup.  Sprinkle the orange zest into the syrup. Stir and allow to steep for at least 10 minutes. Strain into a covered container.  You can store this in your refrigerator for up to one week.

For the cocktail:  In a cocktail shaker, place the lime pieces and the mint leaves.  Pour in the cooled simple syrup and, using a muddler, crush the lime and mint into the liquid for about 20 seconds.

Pour in the rum and blood orange juice.  Top your shaker with a few ice cubes.

Shake the mixture until the outside of your shaker starts to feel very cold.

Strain into a low ball glass.  Top with a splash of sprite or ginger ale.

Garnish with mint and orange slices.