In a heavy bottomed glass, muddle together blackberries, mint, and lime until they have released all their juices. Strain through a fine mesh sieve into a clean rocks glass, being sure to press out all the liquid with the back of a spoon.
Add the honey and stir until dissolved.
Add the gin and a handful of crushed ice. Top with club soda and garnish with a sprig of mint, a blackberry, and/or a slice of honeycomb if desired.