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 the pomegranate aril and simple syrup mixture through blender.
Strain through fine mesh strainer.
Discard the seed solid and keep the pink pomegranate simple 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.