For the Strawberry-Fennel Soda:
In a large saucepan over medium-low heat, combine sugar and water. Add fennel and simmer 10 minutes. Add strawberries and simmer 10 minutes. Remove from heat and strain syrup through chinois. Make soda base by combining 1 part cold water to 4 parts syrup. Transfer to soda siphon and charge.
To Assemble and Serve:
In a shaker, combine gin, vermouth, and lemon juice and shake. Pour into Collins glass filled with crushed ice. Add 2 ounces Strawberry-Fennel Soda. Top with a scoop of Fernet ice cream and a strawberry.