For the Tzatziki
2 Persian or mini cucumbers, coarsely grated
1 cup full-fat Greek yogurt
1 tablespoon olive oil
1 tablespoon lemon juice, plus more as needed
2 teaspoons honey, plus more as needed (optional)
1 garlic clove, grated
Kosher salt and black pepper
For the Salad
2 1/2 pounds small red, new or fingerling potatoes, washed and halved (or cut into 1-inch pieces, if large)
3 Persian or mini cucumbers, sliced into 1/4-inch rounds
1/3 cup black olives, such as Kalamata or oil-cured, pitted, and torn in half if large
1/4 cup chopped dill
1/4 cup chopped mint
Extra-virgin olive oil, for drizzling
To make the tzatziki, place grated cucumber in a colander over the sink and squeeze vigorously to remove any excess moisture. Transfer to a large bowl and stir in the yogurt, olive oil, lemon juice, honey (if using), garlic, 3/4 teaspoon salt and 1/4 teaspoon pepper. Taste and adjust seasonings; it should be tart, savory and a little sweet. Add more salt, pepper, honey and lemon juice accordingly; set aside.
Bring a large pot of salted water to a boil. Add the potatoes and simmer over medium-high for 12 to 15 minutes until just tender. Drain and allow to cool for 8 to 10 minutes until they are just warm to the touch.
Prepare the salad: In a large bowl, combine the cooked potatoes with the tzatziki, sliced cucumbers, olives, dill and mint; season generously with salt and pepper. Drizzle with olive oil, squeeze the lemon on top and serve. Store leftovers in a covered container, chilled, for 1 to 2 days.