Heat the water to 75–80°C (167–176°F), do not boil. Add the jasmine tea and steep for 2–3 minutes maximum. Remove the tea bags or strain the leaves and let the tea cool to lukewarm.
Peel the peaches, remove the pits, and cut into chunks. Blend briefly until smooth. Strain through a fine-mesh sieve into a bowl or measuring jug. Do not press the pulp. Discard solids. You want clean, aromatic peach liquid — not baby food.
While the tea is still warm, stir in 1½ tablespoons honey until fully dissolved. Taste and add up to ½ tablespoon more only if needed. This should stay light and floral, not sweet.
Stir 120–160 ml of the strained peach purée into the tea. Taste and adjust carefully — peach should support jasmine, not sit on top of it.
Refrigerate for 1–2 hours until fully cold and integrated.
Fill glasses with ice, pour over the chilled peach jasmine iced tea, and garnish with fresh peach slices.