In a large bowl, mix lemon zest, tomato paste, coriander, cumin, paprika, black pepper, turmeric, cayenne, cinnamon, 2 Tbsp. yogurt, 2 Tbsp. oil, and 2 tsp. salt. Add chicken and toss to coat. Let marinate 30 minutes.
Meanwhile, in a small bowl, whisk garlic, tahini, lemon juice, 2 Tbsp. oil, and remaining ½ cup yogurt. (This can also be done in a food processor for extra fluffiness.) Stir in 2 Tbsp. parsley. Refrigerate until ready to use.
In a medium bowl, toss cucumbers, tomatoes, a heavy pinch of salt, and remaining ¼ cup parsley. Refrigerate until ready to use.
Arrange a rack in lower third of oven; preheat to 425°. In a small bowl, toss onions, ½ tsp. salt, and remaining 1 Tbsp. oil until onions are coated. Transfer onion mixture to a large baking sheet. Arrange marinated chicken around onion wedges in a single layer.
Roast chicken until cooked through and some lightly charred bits form, and an instant-read thermometer registers 165°, about 25 minutes.
Top with tahini yogurt sauce and cucumber mixture. Serve with pita alongside.
