In large plastic bag or container, add spice mix, juice of a lemon half, sliced onion, half of the garlic, and 1 Tbsp olive oil. Add chicken and shake to coat. Marinate overnight or up to 1 hour in fridge.
In medium bowl, whisk together tahini paste, juice of a lemon half, and remaining garlic until thick. Slowly whisk in 3 Tbsp warm water until consistency is smooth and pourable. Add salt and pepper to taste.
Bake or grill chicken. Arrange marinated onion, chicken, juices/spices in a single layer on foil-lined baking sheet or grill pan. Season with salt and pepper. Bake about 15–20 minutes or grill until no longer pink.
While chicken cooks, tear bread into 4–6 large pieces, then stack and wrap in foil. Place in oven to warm until ready to serve.
In medium bowl, stir together juice of remaining lemon, minced onion, tomato, cucumber, parsley, and 1 Tbsp olive oil to make the salad. Add salt and pepper to taste.
Thinly slice chicken. Divide salad and bread evenly between two plates. Add chicken and roasted onions. Drizzle over tahini mixture and serve.
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