In a small saucepan, combine the honey and warm water and heat gently to about 60–70°C (140–160°F), never boiling, just enough to loosen the honey and make it fluid. Add the rosemary sprig, ginger slices, and jalapeño, keep the mixture at gentle warmth for 15–30 minutes, then remove from heat, cover, and let steep for an additional 30–60 minutes until aromatic with soft heat and herbal depth.
Strain the infused honey through a fine-mesh sieve into a clean jar or bowl, discard all solids, stir in the pinch of fine sea salt, and let the infusion cool completely; it should smell spiced and floral, not aggressive.
In a pitcher, combine 120 ml of the cooled spiced honey infusion with plenty of ice, then add the chilled club soda and stir gently once or twice only to integrate without killing carbonation.
Pour into ice-filled glasses and garnish with rosemary sprigs, ginger slices, and optional jalapeño slices, then serve immediately while cold and lively.
