Add the cumin, coriander, black pepper, allspice, and nutmeg to a small jar. Cover it tightly and shake well until everything is evenly combined. Set this aside since you'll use it for both the chicken and the dressing.
In a small bowl, whisk the lemon juice, olive oil, garlic, tahini, and a pinch of the spice blend until smooth. If you want it extra creamy, blend it in a mini food processor instead. This dressing keeps well in the fridge for up to a week.
Stir the salt and sugar into the lemon juice in a medium bowl until dissolved. Toss in the sliced red onion and let it sit while you prep everything else. Even 15 minutes softens the onion's sharp bite nicely.
Rub the chicken breasts generously with salt and about 2 tablespoons of the spice blend. Grill or broil for roughly 6 minutes per side, until firm and cooked through. Let it rest for 10 minutes before slicing into bite-sized chunks.
In a large bowl, combine the tomatoes, cucumbers, green onions, and drained pickled red onion. Finely chop the fresh herbs together and add them in, along with the romaine, arugula, feta, Aleppo pepper, and a pinch of salt.
Add the sliced chicken to the bowl and drizzle with about half the dressing, tossing everything to coat. Spread a spoonful of yogurt on each plate, pile the salad on top, and serve with warm pita on the side.