Combine seasonings for chicken including cumin, coriander, turmeric, salt, pepper, and cayenne in a small bowl. Drizzle olive oil on chicken and sprinkle both sides with seasoning mix. Place chicken on a baking sheet and put in the oven. Preheat to 425 degrees F. When oven comes to temperature, set timer for 20-25 minutes. Cook until chicken juices run clear and the skin is golden brown.
Meanwhile, make the sauce. Heat 2 tablespoons olive oil in a medium saute pan over medium heat. Saute chopped shallots and garlic for 1 minute, stirring frequently. Add bruised lemongrass stalk, white miso, and yellow curry paste, and saute another minute. Add coconut milk and bring to a simmer. Reduce heat to low and continue to simmer for 5 minutes.
Season the sauce with fish sauce and brown sugar. Simmer for another 1 minute. Finish with a squeeze of lime.
Pour sauce onto serving platter and place chicken on top. Garnish with fresh cilantro and Thai basil. Serve immediately.