Wash and grate the cucumber. Transfer it to a colander and press to remove excess moisture.
Peel and finely mince or grate the garlic.
In a large bowl, combine the Greek yogurt, drained cucumber, garlic, extra-virgin olive oil, white wine vinegar (or juice of 1/2 lemon), and chopped fresh dill.
Season with salt and freshly ground black pepper to taste, then stir until well combined.
Cover with plastic wrap and refrigerate for at least 30 minutes before serving.