Place a heavy-bottomed pot over medium-high heat. Add olive oil to coat the bottom of the pot. Sprinkle the chicken on both sides with salt and pepper and add to the pot, skin-side down. Cook until deeply golden brown, 3 to 5 minutes per side, then mix in the garlic, ginger, coriander, turmeric and cayenne. Briefly saute, then add 8 cups chicken stock. Bring to a simmer, then cook until the chicken is cooked through, 20 to 30 minutes. Remove from the heat and strain, reserving the chicken. When the chicken is cool enough to handle, pull the meat and discard the skin and bones. Add back to the broth along with the fish sauce and bok choy. Keep warm.
Place a medium saucepan over medium-high heat. Add the jasmine rice and remaining 2 cups chicken stock and season with salt and pepper. Bring to a strong simmer, then reduce the heat to low, cover and cook until the rice is tender, about 15 minutes. Remove from the heat and let stand for 5 minutes.
Meanwhile, scrape the coconut cream off the top of the coconut milk. (If there is no separation, refrigerate the can of coconut milk for 1 hour; save the remaining coconut milk for another use.) Fold the coconut cream into the rice, then place quenelles (small oblong dollops) of rice in serving bowls.
Garnish the rice with the sliced scallions, chiles and torn Thai basil. Ladle the chicken around the rice along with the broth. Serve with squeezes of lime.