Remove all the outer leaves that are on each of the cauliflower heads. Cut off the stem at the bottom of each cauliflower.
You want the cauliflower to stand up on a flat base when set down.
Set each cauliflower head on its base. Cut the sides off the cauliflower. Cut the rest of the cauliflower into 3 medium-sized steaks. You want them to be large enough, so they stay intact on the grill.
In a medium bowl, mix the extra virgin olive oil, lemon juice, garlic, paprika, oregano, thyme, za'atar or sumac (optional).
Heat a grill to medium (about 350°F).
Place the cauliflower steaks on a large cutting board or two large plates. Brush each side of the cauliflower with the olive oil mixture and sprinkle and dash of salt and pepper on each side.
Set the cauliflower steaks on the grill and close the grill.
Grill for 5-7 minutes on each side. You want the cauliflower to just begin to char and become tender.
Remove from the grill and sprinkle feta cheese and fresh parsley on the cauliflower steaks.
In a medium mixing bowl, combine the yogurt, tahini, lemon juice, salt and pepper and whisk well.
Drizzle the yogurt tahini sauce over the cauliflower steaks. Enjoy!