Heat the water to 75–80°C (167–176°F), do not boil. Add the white tea and steep for 3–4 minutes. Remove the tea bags or strain the leaves and let the tea cool to lukewarm.
In a small saucepan, combine the peach slices, sugar, water, and rosemary sprig. Bring to a very gentle simmer over medium-low heat and cook for 8–10 minutes, just until the peaches soften and the syrup becomes lightly fragrant. Do not reduce aggressively. Remove from heat and let steep for 5 minutes only.
Strain the syrup through a fine-mesh sieve into a bowl or measuring jug. Do not press the solids. Discard the peaches and rosemary and let the syrup cool completely.
While the tea is still slightly warm, stir in 120–160 ml of the cooled peach rosemary syrup. Taste and adjust cautiously — this drink should stay light and floral, never syrupy.
Refrigerate the tea for 1–2 hours until fully cold and integrated.
Fill glasses with ice, pour over the chilled rosemary peach white iced tea, and garnish with thin peach slices and a fresh rosemary sprig.
