Preheat the grill to medium heat and rub a grill basket with 1 teaspoon olive oil; place the empty basket on the grill to heat.
In a large bowl, toss the eggplant wedges, sliced zucchini, and red onion with the remaining 1 teaspoon olive oil and a pinch of salt and pepper until evenly coated.
Mix the ground cumin, cinnamon, paprika, and allspice. Rub the spice blend onto both sides of the chicken breasts, sprinkle with salt and pepper, and lightly coat with olive oil.
Place the vegetables in the hot grill basket and put the chicken directly on the grill beside the basket. Grill the chicken about 10–12 minutes total, flipping once halfway through; when flipping the chicken, stir the vegetables.
Once the chicken is cooked through, transfer it to a plate and tent with foil to keep warm. Increase the grill to medium-high and continue grilling the vegetables 7–10 more minutes, stirring once, until tender and slightly charred.
Return the cooked vegetables to the large bowl. Add the chopped tomato, halved cucumber, chopped cilantro, and sliced mint. Add the lemon juice and tahini, then toss until the vegetables are evenly coated and creamy.
Slice the chicken breast. Divide the vegetables and chicken between two bowls, then top each with Kalamata olives and chopped pistachios. Serve immediately.