Spread coarse sugar on a shallow plate. Wet an outside rim of a highball or a hurricane glass with orange wedge. Dip the glass into the sugar to coat the edges. Fill the glass with large chunks of ice.
In a Boston shaker, combine Arrogante Reposado, Cointreau liqueur, simple syrup and freshly squeezed lime and orange juices. Add a handful of ice and and shake vigorously for 10 to 15 seconds. Strain the cocktail into the prepared glass.
Slowly add grenadine and wait for it to settle in the bottom of the glass to create the "sunrise" effect. Garnish the drink with a slice of orange and a small sprig of fresh mint.