Remove pulp from lemon with a sharp knife and discard, saving peel. Lightly rinse peel with cool water. Slice off a thin sliver of peel and set aside for garnish.
Combine lemon peel and gin in a shaker. Muddle lemon until slightly crushed. Add 1 cup ice to the shaker, cover, and shake until chilled, 15 to 20 seconds.
Fill a rocks glass with ice and strain cocktail over the ice. Top with tonic water. Garnish with lemon sliver and rosemary sprig.