Place the pomegranate arils into a serving dish and set aside.
Over medium-high heat, combine the sugar, gin, and pomegranate juice in a medium-size saucepan.
Add the rosemary stalks after pinching and twisting each between your fingers to release the essential oils.
Bring the mixture to a boil while stirring to dissolve the sugar. Once the sugar has dissolved, remove the pot from the stove and allow to cool completely. Leave the rosemary in the liquid to allow it to steep.
Strain the simple syrup into a carafe, or glass jar, and set aside until ready to use.
Spoon a tbsp, or two, of the pomegranate arils into a champagne coupe, or flute.
Pour a tbsp and a half, or two (depending on how sweet you like your cocktail), of the simple syrup into the glass. Pour the champagne over the syrup to fill to the rim.
Bruise a stem of rosemary by pinching it between your fingers. Use it to gently stir the cocktail before garnishing the glass with the stem.
Enjoy!