Sprinkle ground saffron on the ice cubes in a small bowl and let it sit on the counter until the ice melts. This will be your bloomed saffron.
In a large bowl, mix the Greek yogurt, onion, olive oil, lemon juice, bloomed saffron, and salt.
Add the chicken pieces to the yogurt and saffron mixture and stir well to mix. Cover the bowl and refrigerate for at least 3 hours or up to 24 hours.
Once ready to grill, take the bowl out of the fridge and place it on the counter. Let it sit for about 30 minutes to come to room temperature.
Meanwhile, heat the gas or charcoal grill.
Thread the chicken pieces onto skewers (make sure to separate the onions) and grill for abut 6 to 7 minutes on each side until they are golden brown on the outside and white and juicy on the inside. (You can turn the skewers a few times to make sure they're nicely grilled and golden on all sides.) Check one piece of the saffron chicken kebab by cutting it with a knife; if it's white and juicy on the inside, it's ready.
Serve with fresh lavash or pita bread and some shirazi salad on the side.