Toss 1 thinly sliced medium English cucumber and ¼ teaspoon kosher salt together in a fine-mesh strainer. Fit over a medium bowl and let sit for at least 10 minutes to draw out excess moisture.
Transfer the cucumbers to a large bowl; discard the liquid. Add 1 pound thinly sliced red radishes, 2 ounces finely grated Parmesan cheese, 1 teaspoon finely grated lemon zest, and 2 tablespoons lemon juice. Toss to combine.
Transfer the salad to a serving plate. Sprinkle with 1 teaspoon finely chopped fresh dill fronds, ½ teaspoon finely chopped chives if using, ¼ teaspoon black pepper, and flaky salt if using. Lightly drizzle with extra-virgin olive oil if desired.
