In a small saucepan, bring 1/4 cup water, 1/4 cup sugar and cinnamon sticks to a boil over high heat. Once sugar is dissolved, remove from heat and steep for 30 minutes. Remove cinnamon sticks before using the simple syrup.
To make the cocktail, combine bourbon, lemon juice and cinnamon simple syrup in a shaker filled with ice.
Strain into a glass filled with ice and garnish with a cinnamon stick.