Make the rosemary simple syrup: Add the sugar, water, and rosemary to a small saucepan and bring to a boil over medium-high heat. Once boiling, reduce the heat to low and simmer for 5 minutes, until the sugar has dissolved. Remove the pot from the heat and set aside to steep for 30 minutes.
Strain into a glass jar, discarding the rosemary. The simple syrup will keep in the refrigerator for up to 1 month.
Make the rosemary Aperol spritz: In a large pitcher, combine the ice, Aperol, prosecco, club soda, and rosemary simple syrup. Add the orange wheels and rosemary sprigs. Pour into large wine glasses filled with ice and serve. For single drinks add 1 cup (150 g) of ice, 3 oz (90 ml) Aperol, 3 oz (90 ml) of prosecco, 1 oz (30 ml) club soda, 1 oz of rosemary simple syrup to a wine glass and stir.