1) In a medium saucepan, combine the rosemary sprigs, sugar and water, and bring to a simmer. Let cook for about 10 minutes until slightly thickened and well-infused.
2) Remove from heat and strain. Discard rosemary sprigs. Let cool before using.
3) In a large pitcher, combine cooled syrup, peach nectar, peach slices and lemon juice ice cubes. Add enough water (about 360 ml) to top off, leaving room for additional ice cubes to serve.
4) Add more ice right before serving. Serve a fresh rosemary sprig in each glass.