Add water, ginger, lime juice, pomegranate juice and sugar to a medium saucepan over medium heat, stirring until the sugar has dissolved. Stir in pomegranate seeds and mint leaves and bring to a boil. Reduce heat and simmer until pomegranate seeds are soft, for about 4-5 minutes. Turn off heat and let the mixture cool.
Discard mint leaves and pomegranate seeds after the mixture has cooled.
Strain the mixture through a cheesecloth. Place in the fridge and use when ready to mx into cocktails.
Ginger Pomegranate Mojito:
In a 10-ounce glass, stir together simple syrup, pomegranate juice and white rum. If you want the mojito sweeter, add more simple syrup.
Add 1/4 cup crushed ice. Rub mint leaves over rim of glass, then tear leaves in half and add to glass. Gently stir for 15 seconds, add the remaining crushed ice, and club soda.
Gently stir for 5 seconds, then tuck mint sprigs into top of glass, garnish with pomegranate seeds and lime on the rim of the glass.