Place the yoghurt into a bowl and add the olive oil, crushed garlic and white pepper. Stir until well combined.
Drain the cucumber and place it into a clean tea towel or muslin. Squeeze well to remove any excess moisture.
Drizzle with a little extra virgin olive oil to serve.
Adapted from the Tzatziki recipe in the book, "The Summer of my Greek Taverna", a memoir by Tom Stone (p. 206).