In a blender, add the peeled and seeded cucumber, water, and honey. Blend until smooth. Optionally, you can strain the mixture through a fine metal sieve for a cleaner mix, but it's fine without straining it as well.
COCKTAIL
Add gin and cucumber mix to a shaker. Shake well with ice.Strain into a clean glass with ice.
Top with club soda and garnish with mint, lime, and cucumber slices.