Step 1: In a large bowl, whisk together the lemon juice, 2 tbsp olive oil, minced garlic, oregano, cumin, coriander, paprika, cayenne pepper (if using), 1/2 tsp salt, and 1/4 tsp black pepper.
Step 2: Add the chicken pieces to the marinade, ensuring all pieces are well coated. Cover and refrigerate for at least 30 minutes, or ideally 4-6 hours, or overnight.
Step 3: Rinse the Basmati rice thoroughly under cold water until the water runs clear. Drain well.
Step 4: In a medium saucepan, melt the butter over medium heat. Add the turmeric powder and saffron (if using) and cook for 30 seconds, stirring until fragrant.
Step 5: Add the rinsed rice to the saucepan and stir to coat. Pour in the chicken broth (or water) and add the remaining 1/2 tsp salt. Bring to a boil, then immediately reduce heat to low, cover tightly, and simmer for 15 minutes. Do not lift the lid.
Step 6: Remove the pan from heat and let it sit, still covered, for another 10 minutes. Fluff gently with a fork before serving.
Step 7: In a small bowl, whisk together the mayonnaise, Greek yogurt, white vinegar, 1 tbsp water/milk, sugar, dried dill (or oregano), and remaining 1/4 tsp black pepper. Taste and adjust seasonings. Add more water/milk if a thinner consistency is desired.
Step 8: Heat a large skillet or griddle over medium-high heat. Add the remaining 1 tbsp olive oil. Once hot, add the marinated chicken pieces in a single layer (cook in batches if necessary).
Step 9: Cook the chicken for 5-7 minutes per side, or until deeply golden brown and cooked through, with slightly charred edges. You can press down on the chicken with a spatula to encourage searing. Remove from pan and chop or shred into bite-sized pieces.
Step 10: To serve, place a generous portion of yellow rice on a plate. Top with the cooked chicken. Drizzle generously with the white sauce, and add a zig-zag of hot sauce if desired. Garnish with fresh parsley or cilantro and serve immediately.