Put the chicken cubes on a baking sheet and put in the freezer until very firm, about 30 minutes. Put the blade and bowl of a food processor in the freezer as well.
Meanwhile, mix together the cumin, paprika, turmeric, garlic, allspice, chili, cinnamon and 1 tablespoon salt in a bowl. Mix in the olive oil to make a paste.
Working in 2 batches, put the firm, almost-frozen chicken into the cold food processor and pulse 10 to 15 times until coarsely chopped. Transfer the chopped meat to a bowl and repeat with the remaining chicken cubes. Add the spice blend paste to the meat and mix to gently combine. Divide the meat into 4 balls and flatten into 3/4-inch-thick patties.
Prepare a grill for medium-high heat. Clean and oil the grates. Brush each patty with some oil, then season with a bit of salt and pepper. Grill until the inside of the patties registers 160 degrees F, about 5 minutes per side. Let the burgers rest for 5 minutes. Butter and toast the rolls.
Burger Build: On each roll bottom, place 1 leaf of romaine, then a burger and some giardiniera. Add a nice schmear of the Lemon Tahini sauce on each roll top.
Vigorously whisk the tahini, lemon zest and juice, honey, olive oil and 2 tablespoons water together in a bowl until smooth and creamy. Season with salt and pepper.