The secret to perfect Tzatziki is using really thick Greek yogurt and thoroughly removing all the water from the cucumber. If you don't remove the water, the sauce will be too runny.
Tzatziki's flavor improves when allowed to rest in the refrigerator, as the garlic and yogurt flavors meld together. It is traditionally served drizzled with olive oil and a sprig of dill or mint.
Wash, peel, and coarsely grate the cucumber. (Some Greeks finely dice it, but grating is more common.)
Place the grated cucumber in a sieve, salt it well, and let it sit for 10 minutes. The salt will draw out the water.
Then, thoroughly squeeze the cucumber by hand, or wrap it in a clean cloth and wring out the excess liquid. This is a crucial step for the Tzatziki's thickness!
Place the thick Greek yogurt in a bowl. Add the squeezed cucumber, crushed garlic, lemon juice, and 1 tbsp of olive oil.
Mix well. Season with salt and black pepper to taste. If using, stir in the dill.
Cover the sauce and chill in the refrigerator for a minimum of 1 hour, ideally 4 hours, to allow the flavors to meld.
If you desire an even thicker sauce, you can strain the yogurt in a cheesecloth for 30 minutes before using to remove excess whey.
Transfer the Tzatziki sauce to a serving bowl.
Before serving, drizzle with the remaining tablespoon of olive oil and optionally garnish with mint or dill leaves.
Serve with Souvlaki, Gyro, grilled vegetables, or as a dip for pita bread.