In a small saucepan, combine the water and sugar and heat gently, stirring until fully dissolved without boiling; remove from heat, add the lemon zest, cover, and let steep for 10–15 minutes until aromatic, then strain and let the syrup cool completely.
Add the lemon pulp, fresh lemon juice, 120 ml of the peel-infused syrup, mint leaves, pinch of fine sea salt, ice-cold water (start with 2½ cups), and ice cubes to a high-speed blender.
Blend on high until completely smooth and slushy, then taste and adjust carefully by adding more water if too thick, more ice if too thin, and a little more syrup only if needed; the final total water should land around 4 cups when accounting for melted ice.
Pour into chilled glasses and garnish with lemon slices and fresh mint leaves, serving right away.
