To make rosemary syrup: Simmer 1/2 cup sugar, 1/2 cup water, and a rosemary sprig for 5 minutes, then cool and strain.
Fill a glass with ice. Add cranberry juice and rosemary syrup. Stir to combine.
Add prosecco and club soda. Stir gently to keep bubbles.
Garnish with a rosemary sprig and fresh cranberries. Serve cold.
Notes
Rosemary syrup can be made ahead and stored in the fridge. Adjust syrup for sweetness and prosecco for fizz. For a less boozy version, use extra club soda instead of prosecco.