Mix yogurt, lemon juice, oil, garlic, tomato paste, salt, oregano, pepper, allspice, cinnamon, and cardamom in a large bowl. Add chicken and toss to coat; transfer into a resealable plastic bag, squeeze out excess air, and seal the bag. Marinate in the refrigerator for 4 hours.

Preheat an outdoor grill for medium-high heat and lightly oil the grate.

Thread chicken, onions, and bell pepper onto metal skewers.

Cook on preheated grill until chicken is golden and no longer pink in the center, about 5 minutes on each side. Sprinkle parsley over the skewers.