In a small saucepan, combine the water and sugar and heat gently, stirring just until the sugar fully dissolves; do not boil. Remove from heat, add the lime peel, and let steep for 10–15 minutes until aromatic, then strain out the peel and let the syrup cool completely.
Add the frozen strawberries, white verjus, fresh lime juice, 60 ml of the cooled syrup, and the ice to a high-speed blender, then blend until thick, smooth, and slushy.
Taste and adjust the balance if needed — add more syrup for sweetness, more lime juice for sharpness, or more ice for a thicker, colder texture.
Pour into chilled glasses and garnish with optional lime slices and whole strawberries pressed against the glass; serve immediately while fully frozen and vibrant.