Soak skewers in water 30 minutes. Meanwhile, place bread and water to cover in a small bowl; let stand 10 minutes. Using hands, squeeze excess liquid from bread; transfer bread to a large bowl. Stir in beef and next 9 ingredients.
Coat cold grill grate with cooking spray. Preheat grill to 400° (medium-high) heat. Divide ground beef mixture into 8 portions, and chill 10 minutes. Press and flatten each portion around a skewer, forming a 4- to 5-inch oval.
Grill, covered with grill lid, 7 to 8 minutes or until golden brown, turning once. Serve warm with pita rounds, Yogurt-Tahini Sauce, and Herbed Cucumber-and-Tomato Salad.
MAKE IT AHEAD Prepare these kabobs up to two days in advance, and store in the fridge. Pop them on the grill just before you're ready to serve.