Wash and trim the cucumber and coarsely grate the flesh, including the skin.
Stir in 1 tsp salt, then leave to stand for about 10 minutes.
Pour off any liquid that has formed, then place the grated cucumber in a sieve and gently squeeze out the remaining excess water.
Peel the garlic.
Wash the mint and shake dry.
Transfer the cucumber to a bowl and mix in the yogurt.
Press the garlic into the bowl through a garlic presser, add the vinegar and olive oil, and stir well.
Season with salt and refrigerate for about 10 minutes.
Serve chilled, garnished with min leaves.