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Start by making a syrup: put the white caster sugar in a medium-sized saucepan along with 50ml water, the fennel seeds and the celery seeds. Stir and cook gently over a really low heat until all the sugar has dissolved. Remove from the heat, allow to cool for 10 mins, then add the lime juice.
Strain the fennel and lime syrup through a fine sieve into a cocktail shaker, add the gin and a handful of ice, then shake to combine. Once the outside of the cocktail shaker feels cold, strain the mixture into 4 Martini glasses. Add a wedge of baby fennel to each glass, then serve.