Add gin, lemon juice, rosemary syrup, cranberry or pomegranate juice, and egg white to a shaker.
Dry shake (no ice) for about 15 seconds to foam the egg white.
Add ice and shake again until well chilled.
Strain into the chilled glass.
Top with club soda.
Garnish with rosemary sprig and cranberries or pomegranate seeds.
Notes
Adjust syrup for sweetness. Use fresh lemon juice. For more herbal flavor, steep rosemary syrup longer. Omit egg white for a lighter drink. Use a coupe or rocks glass. Swap cranberry for pomegranate as desired.