Process garlic, egg whites, lemon zest and lemon juice in a food processor or blender until frothy and smooth. With motor running, slowly stream in half of the oil.
Combine ¼ cup of the prepared toum, lemon juice, tomato paste, coriander, paprika, and 3 tablespoons of olive oil in a large ziplock style bag. Squeeze the bag to mix the ingredients.
While the chicken is resting prepare the cherry tomatoes by combining tomatoes, olives, olive oil, garlic salt and pepper on a foil-lined sheet pan.
Place sheet pan on the grill and roast tomato mixture for 5-8 minutes, stirring once halfway through. Tomatoes should be shiny, but not bursting open.
Combine ½ cup of the toum with ½ cup Greek yogurt and stirl until nice and smooth. Reserve the remaining toum for another use (see the post above). Serve chicken with pitas, toum/yogurt mixture, Zhoug (optional), lemon wedges, and fresh cilantro sprigs.
See Café Tips above in the post for more detailed instructions and tips.
Nutritional info does not include Toum.
Adapted from Bon Appetit.