Slice an inch of each cucumber end and discard. Slice cucumber into chunks, then grate each (skin, seeds and all) against the largest hole of a box grater.
Place the grated cucumber in a sieve, sprinkle over ½ tsp of salt, mix together and then leave to drain for 15 minutes over the top of a bowl.
Remove the mint leaves from the stem. Discard the steam and finely chop the leaves.
Add the cucumber and mint to the yoghurt and mix until evenly incorporated.
Taste test and adjust seasoning (if desired). Serve in the bowl as is, or spoon into another serving dish.