Peel the cucumber and chop it roughly into two parts. If you use a regular cucumber, cut it lengthwise into half and scoop out the seeds. I left the seeds since I used an English cucumber. Grate each part using a box grater. Place the shredded cucumber in a fine-mesh sieve lined with cheesecloth, sprinkle 1/4 tsp salt and leave it aside for 10-15 minutes.
Meanwhile, add the Greek yogurt in a mixing bowl, also add olive oil, minced garlic, vinegar or lemon juice, salt, and pepper. Give everything a good mix using a whisk or spoon. Refrigerate if required while the cucumber shreds are draining.
After 15 minutes, bring the edges of the cheesecloth together and squeeze out as much of the water as possible out of the cucumber. Will yield about 7.5 oz approx or 1 cup packed shredded, drained cucumber.
Transfer the drained, shredded cucumber to the yogurt mixture. Also, add the chopped dill, and mix everything well once again. Taste and adjust with more salt if required.
Serve immediately or cover the bowl with a cling wrap, and refrigerate for 1 hour for flavors to mingle. Transfer the tzatziki to a serving bowl, drizzle some more extra virgin olive oil, garnish with dill leaves. Serve with pita bread or pita chips or carrot sticks, sliced bell peppers. You may refrigerate tzatziki for up to 2 days. If it is stored longer, it might turn watery and lose the thick texture. Remember to cover the bowl while storing in the refrigerator.