Position a rack in the upper part of the oven and preheat the broiler. In a large bowl, combine the lamb, 1/4 cup parsley, the mint, onion, two-thirds of the garlic, the tomato paste, coriander, paprika, cumin, cinnamon and lemon peel; season with salt and lots of pepper. Divide the meat mixture into 4 equal sections. Mold the meat in the shape of a log around 4 skewers. Drizzle with a little EVOO and place on a broiler pan. Broil the meat, turning once, for about 12 minutes.
In another large bowl, combine the cooked bulgur, the red onion, spinach, arugula, tomatoes, remaining garlic and 1 cup parsley and two-thirds of the lemon juice. Dress with 1/4 cup EVOO; season with salt and pepper.
In a small serving bowl, mix the tahini with about 3 tablespoons water. Stir in the yogurt.
Douse the kebabs with the remaining lemon juice. Slide the meat off the skewers and cut each log lengthwise into thirds. Pass the meat, tabbouleh salad, yogurt sauce and pitas around the table.