For the cinnamon syrup: Combine the sugar and 1 cup water in a small saucepan. Bring to a simmer and stir until the sugar is completely dissolved. Add the cinnamon sticks and continue to simmer until the flavors are infused, 15 to 20 minutes. Cool, then strain and discard the cinnamon sticks. Refrigerate in an airtight container for up to 2 weeks.
For the mojito: Add the mint, lime wedges and 1 ounce cinnamon syrup to a cocktail shaker and muddle. Fill with the ice, and add the rum and orange juice and shake briefly. Pour directly into a highball glass. Top off with the sparkling wine and stir briefly. Garnish with a mint sprig and blood orange slice.