Preheat oven to 400°F.
In a small bowl, stir together cumin, garlic powder, pepper, allspice, salt, smoked paprika,cinnamon, and cardamom.
Place chicken on a rimmed baking sheet. Drizzle with olive oil, rubbing to coat evenly.
Using your fingers, gently loosen skin from meat. Sprinkle outside of chicken liberally with spice blend. Rub remaining spice blend under skin.
Bake until chicken is cooked through, 25 to 30 minutes. Let cool slightly.
In a small bowl, whisk together tahini, lemon juice, garlic powder, salt, and cumin.
Whisk in warm water, 1 tablespoon at a time, until dressing is smooth and reaches desired consistency.
When chicken is cool enough to handle, remove skin, and set aside.
Pull meat from the bones; discard bones. Chop chicken. If desired, pour drippings form baking sheet into a medium skillet, and heat over medium heat.
Add pulled chicken and skins (if desired) to skillet; cook until crispy, about 3 minutes. Drain chicken, and discard drippings.
To serve, divide chicken mixture among four bowls. For each bowl, tuck in 1 romaine wedge half, and about half a cup each cucumber and tomatoes. Drizzle with dressing; sprinkle with feta, parsley leaves, and cayenne, if desired. serve with pita bread.