Combine vodka and fennel seeds in an air tight container, preferably a glass jar with a airtight seal lid. Set on the counter for 48-72 hours, or longer if you prefer a stronger fennel taste. Strain the fennel seeds from the vodka, and then rinse out any seeds that remain in the original storage container. Return vodka to the airtight container and leave at room temperature until ready to make cocktails.
Combine water, honey and peaches in a small saute pan over medium heat. Simmer for about 5-10 minutes, stirring occasionally, until the honey is completely dissolved. Remove pan from the heat and allow peaches to steep for 20 minutes. Strain peaches from the simple syrup and store syrup in an airtight container in the refrigerator.
In a shaker, combine fennel vodka, simple syrup, tarragon sprig and lemon juice. Fill shaker with ice and shake for 20-30 seconds until well combined. Strain into a cocktail glass and fill with crushed ice. Garnish with tarragon sprig. Enjoy!