In a medium bowl, mix the Greek yogurt, olive oil, lemon, garlic, 3 tablespoons za'atar mix, salt and pepper and stir until combined.
Add the chicken thighs to a large mixing bowl and add the yogurt za'atar marinade. Mix well until the chicken is fully coated. Refrigerate for two hours.
Preheat the oven to 425°F.
In a large mixing bowl, add the potatoes, carrots, red onion, cauliflower, lemon slices. Add the olive oil and the two teaspoons za'atar seasoning and toss the vegetables and potatoes until combined.
On a large non-stick baking sheet, lay out the vegetables and potatoes. Nestle the chicken into the vegetables and potatoes. Sprinkle more za'atar seasoning over the sheet pan meal.
Cover the sheet pan with foil and bake for 20 minutes. Remove the foil and bake the sheet pan another 35 minutes or until the chicken reaches an internal temperature of 165°F.
Remove the sheet pan from the oven and let sit for five minutes. Garnish with fresh parsley and crumbled feta cheese. Serve with couscous.