Thinly slice green onions and finely chop mint and cilantro. Cut washed and drained chicken into eight pieces and keep it aside.
Add plain yogurt, lime zest, juice, and spices in a large mixing bowl and whisk to combine well.
Make one cut into each piece of chicken meat down to the bone. Toss the chicken into the yogurt mixture very thoroughly.
Wrap the chicken meat with plastic cling film and refrigerate it for 8 hours or overnight.
Preheat the oven to 450 degrees F and grease a 9x13-inch casserole dish.
Grind saffron strings in a mortar with a pestle, pour chicken broth and stir to combine.
Now boil unsalted butter, salt, remaining cups of chicken broth and chicken broth-saffron mixture in a saucepan.
Add basmati rice to the mix and stir to combine for 15 minutes. Once cooked, put it aside and rest for 10 minutes.
Transfer cooked rice into the prepared casserole dish and gently spread it into an even layer using a spatula.
Place the refrigerated chicken pieces on top of the rice. Drizzle olive oil and sprinkle salt.
Roast it in the oven until the chicken is no longer pink in the centers and the juices run clear for about 45 minutes.
Mix the remaining yogurt, minced garlic, chopped green onions, mint, cilantro, salt, and water for the sauce. Refrigerate it until it is needed. Serve the chicken and rice and top with sauce.