Prepare the cucumbers: Coarsely grate the cucumbers, sprinkle with ½ teaspoon of salt, and mix well. Set aside for 5 minutes to release their excess moisture.
Prepare the garlic mixture: Press the garlic into a small bowl. Add 1 tablespoon of vinegar, 30 ml of olive oil, and a pinch of black pepper. Stir well and let the mixture rest for a few minutes to mellow the garlic's sharpness.
Drain the cucumbers: Transfer the grated cucumbers to a colander and squeeze firmly with your hands or press with a spoon to remove as much liquid as possible. This is the secret to thick, creamy tzatziki.
Combine the ingredients: In a mixing bowl, add 400 g of thick, strained Greek yogurt, the well-drained cucumbers, and the garlic mixture. Stir thoroughly until everything is evenly combined.
Chill and serve: Cover and refrigerate for at least 20 minutes, preferably up to 1 hour, allowing the flavors to blend and the tzatziki to develop its creamy texture. Serve chilled.