Grate the cucumber coarsely and place the grated cucumber in a fine sieve or clean kitchen towel.
Sprinkle the cucumber with a pinch of salt and let it sit 5–10 minutes to draw out moisture.
Squeeze the cucumber firmly in the towel or press the sieve to remove excess liquid until mostly dry.
Place the strained Greek yogurt in a bowl and stir to loosen to a creamy consistency.
Add the minced garlic to the yogurt and mix thoroughly so the garlic is evenly distributed.
Stir in lemon juice, olive oil, chopped dill (or mint), pepper and optional vinegar or honey.
Fold in the well-drained grated cucumber until evenly combined with the yogurt.
Taste and adjust salt, lemon juice or garlic to suit your preference.
Cover the tzatziki and refrigerate for at least 30 minutes to allow flavors to meld.
Stir once more before serving and drizzle a little olive oil on top if desired.