Fill a large punch bowl with ice.
Add the cognac, mint leaves, ginger slices and cinnamon sticks, then the lime juice and syrups.
Add the ginger ale right before serving in a punch glass with ice.
*Cinnamon syrup: Combine 1 cup sugar and 1 cup water in a saucepan, and boil until sugar is dissolved. Add 6 cinnamon sticks, cover and let it sit overnight. Remove cinnamon sticks.