For the yogurt-mint dressing: Whisk the yogurt, mint, lemon juice, tahini, olive oil, cumin and garlic in a medium bowl and season with salt and pepper.
For the salad: Preheat the grill. Brush both sides of the onion slices with olive oil and season with salt and pepper to taste. Grill on each side for 2 to 3 minutes, just to obtain grill marks and cook slightly. Remove from the grill and coarsely chop. Add the onions, oregano and cucumber to the dressing and toss to coat. Season with salt and pepper to taste. Sprinkle with the feta.