Grate the cucumber (keep the peel if organic). Place it in a sieve with a pinch of salt, let it rest for 10 minutes, then squeeze out excess water using your hands or a clean kitchen towel.
Crush the garlic cloves with a little salt in a mortar until smooth (this gives the tzatziki a velvety consistency).
In a large bowl, add the yogurt. Mix in the cucumber, garlic, olive oil, vinegar, dill, salt, and pepper. Stir gently until well combined.
Refrigerate for at least 1 hour to allow flavors to meld. Serve drizzled with extra olive oil and a sprinkle of black pepper.