Make the Lemon Sauce: In a small bowl combine the parsley, lemon zest and juice, garlic, jalapeno, and salt. Set aside.
For the Chicken Kawarma, dice the chicken. In a large bowl combine the pepper, allspice, cinnamon, oregano, vinegar, mint, parsley and salt. Add the chicken, toss to coat and let marinate at room temperature for about 30 minutes, or in the fridge for about 2 hours.
In a large skillet over medium high heat add about 2 teaspoons of the oil. When hot, add about 1/3 of the chicken mixture and sauté for about 4 minutes, until the chicken is just barely cooked through. Transfer to a plate. Repeat with another 2 teaspoons of oil, and 1/3 of the chicken. Add that to the first batch of cooked chicken. Repeat with the rest of the oil, and the spiced chicken.
Meanwhile, spread the hummus in a thick circle, with the edges a bit higher than the middle (like a rimmed plate made of hummus). You can do this on individual plates if you’re feeling sophisticated,or on a large platter. Pile the chicken mixture into the center of the circle(s) of hummus, drizzle the sauce generously over the chicken, and sprinkle with any desired toppings.