Combine the vegetables: Choose a wide, shallow bowl rather than a deep mixing bowl. Scatter the thick tomato wedges, cucumber half-moons, shaved red onion, and Kalamata olives evenly across the bottom.
Mix the simple dressing: In a small glass measuring cup, combine the extra virgin olive oil, fresh lemon juice, dried oregano, and kosher salt. Whisk vigorously for about 15 seconds until the mixture turns slightly pale and emulsified.
Dress and toss gently: Pour the liquid evenly over the piled vegetables. Using two large wooden spoons, gently lift and turn the vegetables from the bottom six to eight times. You want every slice lightly coated without bruising the tender tomatoes.
Let it rest: Leave the bowl right on the kitchen counter at room temperature for exactly 10 minutes. This short rest allows the salt to draw out natural moisture from the tomatoes, combining with the oil into a fragrant broth.
Add the feta and serve: Take the block of feta out of its brine. Break or slice it into thick, rustic slabs or large broken chunks and lay them over the vegetables. Finish with a final light drizzle of olive oil over the cheese and a tiny pinch of dried oregano before serving.