Make simple syrup by heating 1/4 cup water and 1/4 cup granulated sugar on medium heat until all sugar has dissolved. Remove from heat, add 1/2 cup pomegranate seeds, and allow to cool completely. Run through blender and then strain through fine mesh strainer. Discard seed solid and keep the pink syrup.
To make the cocktail, combine 4 ounces bourbon whiskey, 2 ounces lemon juice, and 2 ounces pomegranate simple syrup in a shaker with ice. Vigorously shake until well combined, about 20 seconds. Strain into a low ball ice with extra large ice cubes.