Chef John's Chicken And Rice Casserole

Ingredients

• ⅓ cup plain yogurt
• 1 medium lime, zested and juiced
• 2 teaspoons kosher salt
• 1 teaspoon ground paprika
• 1 teaspoon ground cumin
• ½ teaspoon ground coriander
• ¼ teaspoon cayenne pepper
• ¼ teaspoon ground white pepper
• ¼ teaspoon ground cardamom
• ¼ teaspoon ground cinnamon
• ¼ teaspoon ground allspice
• 1 (2 to 3 pound) whole chicken, cut into 8 pieces
• 1 pinch saffron
• 2 ¼ cups chicken broth, divided
• 2 tablespoons unsalted butter
• 1 teaspoon kosher salt
• 1 ½ cups basmati rice
• 1 drizzle olive oil
• salt to taste
• ½ cup plain yogurt
• 2 cloves garlic, crushed
• 2 tablespoons thinly sliced green onions
• 2 tablespoons finely chopped mint
• 2 tablespoons finely chopped cilantro
• 1 tablespoon water, or as needed