In a saucepan, add the sugar, water, and corn syrup and cook over medium heat until sugar is dissolved. Add the chopped fennel and cook over medium-low heat for 15 minutes. Then remove from heat and let cool to room temperature. Strain half the fennel from the syrup and set aside for roasting. Store the syrup along with the leftover fennel in an airtight jar or container in the refrigerator.
For the cocktail
Roast strained fennel on a sheet pan at 275° for 30 minutes, or until it reduces by about half in size and is slightly golden in spots. Dust with granulated sugar. Let cool. These don’t stay crispy too long, so use them as a garnish and enjoy the rest (they taste like candy!).
In a cocktail shaker with ice, add the gin, fennel syrup, lime, and bitters and shake until cold. Strain into coupe glass and garnish with a lime wheel, fennel frond, and a piece of candied fennel.