Preheat oven to 350 degrees, with rack in lower third. Toss chicken with curry powder, cayenne, and 1/2 teaspoon salt. In a large Dutch oven or other heavy pot, heat 2 teaspoons oil over high. In batches, cook chicken until browned on all sides, about 12 minutes total. Transfer to a large plate.
Reduce heat to medium and add 1 teaspoon each salt and oil, garlic, ginger, and onion. Cook, stirring and scraping up browned bits with a wooden spoon, until onion is translucent, 6 minutes. Stir in tomato paste and cook 1 minute. Add rice, coconut milk, and 2 cups water; stir to combine and bring to a boil. Arrange chicken in pot, skin side up, cover, and transfer to oven. Bake until chicken is cooked through and liquid is absorbed, about 20 minutes. Sprinkle with cilantro and serve.