Pat the chicken dry and cut it into 1-inch-wide strips. Cut the peppers, onion, and zucchini into sturdy, evenly sized pieces.
Whisk the olive oil, lemon juice, garlic, cumin, coriander, paprika, turmeric, allspice, cinnamon, cayenne, salt, and black pepper in a large bowl.
Add the chicken and toss until evenly coated. Cover and refrigerate for 30 minutes or up to 8 hours.
Preheat the oven to 425°F (220°C). Line a large rimmed sheet pan with parchment paper.
Spread the chicken, bell peppers, red onion, and zucchini in a single layer on the pan. Add the cherry tomatoes around the edges. Avoid overlapping the chicken.
Roast for 20 to 25 minutes, stirring the vegetables once, until the largest chicken pieces reach 165°F (74°C) on an instant-read thermometer.
For deeper caramelization, broil the fully cooked chicken and vegetables for 1 to 2 minutes, watching closely to prevent burning.
Rest the pan for 5 minutes. Squeeze fresh lemon over the chicken, sprinkle with parsley, and serve with optional pita, rice, hummus, or tahini sauce.