Add yogurt, lime zest and juice, salt, paprika, cumin, coriander, cayenne, white pepper, cardamom, cinnamon, and allspice for marinade to a large mixing bowl; whisk to combine.

Make one or two slits into each piece of dark chicken meat, down to the bone. Add chicken parts to the yogurt marinade and toss very thoroughly. Wrap in plastic wrap and marinate in the refrigerator for 4 to 8 hours.

Preheat the oven to 450°F (230°C). Lightly grease a 9x13-inch casserole dish.

Grind saffron in a mortar with a pestle. Pour in 1/4 cup chicken broth and stir to combine.

Combine unsalted butter and salt in a saucepan; pour in remaining 2 cups chicken broth and chicken broth-saffron mixture. Bring to a boil. Add basmati rice and stir to combine. Reduce heat to low, cover tightly, and let simmer for 15 minutes. Turn off heat and let rest for 10 minutes.

Transfer hot rice into the prepared casserole dish. Use a fork to fluff the rice and spread into an even layer. Place chicken pieces, skin-side up, on top of rice. Drizzle with olive oil and sprinkle with salt.

Roast in the oven at 450°F (230°C) until chicken is fully cooked, about 45 minutes. Ensure chicken reaches an internal temperature of 165°F (74°C).

While chicken is cooking, mix yogurt, garlic, green onions, mint, cilantro, salt, and water for the sauce. Refrigerate until ready to serve.