For the sugared cranberries: Combine 1/2 cup of the sugar and 1/2 cup water in a medium saucepan over medium heat; stir until the sugar is dissolved. Add the cranberries and stir until fully covered in the syrup. Using a slotted spoon, transfer the cranberries to a wire rack. Let dry for about 1 hour, or until tacky to the touch.
Strip the leaves from the bottom three-quarters of the rosemary sprigs (to form skewers). Thread 3 sugared cranberries onto each sprig. Roll the cranberries in the remaining sugar to coat. Place on a plate and let dry for another hour. (The skewers can be made a day ahead and kept, covered, in a cool, dry place.)
For the rosemary simple syrup: In a small saucepan, combine the sugar, rosemary sprigs and 1 cup water. Bring to a boil, stirring until the sugar is dissolved. Lower the heat to a simmer and cook for 2 minutes. Turn off the heat and let sit for 30 minutes to cool. Once cooled, discard the rosemary sprigs.
For the cocktail: In a cocktail shaker, combine 1/2 cup rosemary simple syrup and the cranberry juice and ginger beer. Stir gently. Divide between 4 coupe glasses and top off each with 3 to 4 ounces prosecco. Garnish with the sugared-cranberry rosemary skewers.
Recipe courtesy of Tia Mowry