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.
Gently clap the rosemary sprig between your hands to release aroma, then add it to the warm tea. Let infuse for 6–8 minutes only, just until a clear, assertive rosemary aroma develops. Remove the rosemary promptly to avoid piney or medicinal notes.
While the tea is still warm, stir in 2 tablespoons of honey until fully dissolved. Taste and add up to 1 additional tablespoon only if needed. Let the tea cool to room temperature.
Stir in the fresh grapefruit juice. This is the sole source of acidity in the drink, so adjust carefully — it should taste bright and structured, not sharp.
Refrigerate for 1–2 hours until fully cold and integrated.
Fill glasses with ice, pour over the chilled rosemary grapefruit white tea cooler, and garnish with grapefruit wedges and a fresh rosemary sprig.