Peel cucumber in alternating strips to leave about half of the peel on the cucumber. Cut the cucumber in half, and scrape out the seeds and pulp with a spoon. Grate the cucumber on a medium grater, and toss the grated cucumber with the salt. Place the cucumber in a mesh strainer over a bowl to drain for 1-2 hours. Weight the cucumber with another bowl if necessary.
Once the cucumber is drained, fold it into the Greek yogurt, along with the mint, olive oil, lemon juice, garlic, and lemon zest (optional).
Season to taste with extra salt if needed, then let the tzatziki rest in the refrigerator for a few hours before serving.
Recipe by The Taste Edit at https://thetasteedit.com/tzatziki/