Make the spice mix: Put the ingredients for the spice rub in a jar. Cover and shake well to mix.
Make the dressing: Whisk together all ingredients in a small bowl. For a creamier, emulsified dressing blend in a mini food processor or blender.
Make the pickled onion: Put 1/2 teaspoon salt and the sugar in a medium bowl. Add 1 tablespoon of the lemon juice and whisk to dissolve. Add the red onion in the bowl and toss together. Set aside or cover and refrigerate up to 1 day ahead.
Sprinkle the chicken evenly with 1 teaspoon salt and 2 tablespoons of the Shawarma spice rub. Set aside while preparing the vegetables for the salad, or cover and refrigerate up to 1 day ahead.
Put the tomatoes, cucumbers and green onions in a large salad bowl. Drain the red onion and add to the bowl.
Pile the herbs together on a cutting board and finely chop. Add the herbs to the bowl, along with the romaine, arugula, feta, Aleppo chili pepper and a pinch of salt.
Cook the chicken on a medium-hot outdoor grill until firm and no longer pink, about 6 minutes per side. Or cook indoors under a hot, preheated broiler with the oven rack 6 inches from the heat source, about 6 minutes per side. Let the chicken rest 10 minutes, then slice into bite-sized chunks.
Add the chicken to the bowl. Drizzle about half the dressing over and toss to mix. Taste for seasoning, adding more dressing, salt, pepper or chili if you like.
Spread a tablespoon of yogurt on each serving bowl or plate. Serve the salad over the yogurt with the pita on the side.
To make this a vegetarian salad, omit the chicken and use chickpeas instead - try the crunchy roasted chickpeas in this recipe, using 2 teaspoons of the Shawarma rub.The spice rub recipe makes a little more than you'll need to make the salad. Store in a covered jar.