Grind Your Own Chicken Shawarma Burgers

Name: Grind-Your-Own Chicken Shawarma Burgers
Ingredients: 1 pound boneless, skinless chicken thighs, cut into 1-inch cubes; 1 pound boneless, skinless chicken breasts, cut into 1-inch cubes; 1 teaspoon ground cumin; 1 teaspoon sweet paprika; 1/2 teaspoon turmeric; 1/4 teaspoon granulated garlic; 1/4 teaspoon ground allspice; 1/4 teaspoon chili powder; 1/8 teaspoon ground cinnamon; Kosher salt and freshly ground black pepper; 2 tablespoons olive oil, plus more for grilling; Butter, for buttering the rolls; 4 sesame seed kaiser rolls, split; 4 romaine lettuce leaves; 1 cup giardiniera, chopped; Lemon Tahini Sauce, recipe follows; 1/4 cup tahini sauce; Zest of 1 lemon plus 1/4 cup lemon juice; 1 tablespoon honey; 1 tablespoon olive oil