Combine the chopped tomatoes, cucumber, red onion, olives, parsley and a sprinkle of salt and pepper in a small bowl; set aside.
In a blender, combine the chickpeas, lemon juice, 1 tablespoon olive oil, cumin, garlic, tahini and a sprinkle of salt and pepper. Gradually add water (start with 1 cup) and blend until smooth and thin enough to pour. Taste and adjust seasoning. Pour into bowls, and top with the chopped-vegetable mixture, some crumbled feta, a sprinkle of cumin (if you like) and a generous drizzle of olive oil.