In a small saucepan over medium-high heat, stir together the sugar, water and fennel seeds for the fennel syrup. Bring the mixture to a boil, stirring constantly, until the sugar is dissolved. Remove from heat and steep for 30 minutes. Strain into an airtight container. Fennel syrup can be stored in an airtight container in the refrigerator for up to 30 days.

In the bottom of a shaker, muddle mint leaves. Add fennel syrup, vodka, and lemon juice. Fill the shaker with ice and shake well. Pour over ice into a highball glass. Top with soda water.