Combine the sugar, water, and fresh rosemary sprigs in a small saucepan over medium heat. Stir until the sugar dissolves, which takes about 2 minutes. Once the sugar is fully dissolved and you can see the syrup is clear, bring it to a gentle simmer.

Let the syrup simmer with the rosemary for exactly 5 minutes. Set a timer. At 5 minutes the rosemary gives the syrup a soft, fragrant herbal quality. Past that point the flavor shifts toward piney and sharp, which you do not want. Remove the pan from the heat as soon as the timer goes off.

Pour the syrup through a fine mesh strainer into a small bowl or jar. Discard the rosemary sprigs. Let the syrup cool to room temperature before using, about 15 minutes. If you are making this ahead, cover the jar and refrigerate.

Juice your lemons until you have 1/2 cup of fresh lemon juice. Strain out any seeds.

Pour the pomegranate juice, fresh lemon juice, and cooled rosemary syrup into a large pitcher. Stir everything together well. Taste the base. It should be pleasantly tart and sweet with a mild herbal note in the background. Add a little more syrup if you want it sweeter, or another squeeze of lemon if you want more brightness.

Right before serving, pour the sparkling water into the pitcher slowly and stir just once or twice to combine without knocking out all the bubbles. Fill glasses with ice and pour the drink over the top. Garnish each glass with a small rosemary sprig and a pinch of pomegranate arils if you like. Serve immediately while the drink is still bubbly.