Heat the oil in a large skillet over medium-high heat. Add the onion, carrots, celery, garlic and ginger and cook, stirring, until the vegetables soften, about 3 minutes. Add the chicken and cook until golden brown, 3 to 5 minutes. Add the curry powder, stir to coat, and cook for 1 minute. Add the broth and coconut milk and simmer 4 minutes.
Remove from the heat, stir in the cilantro, and season with salt and pepper. Spoon the rice into bowls and top with the mulligatawny stew.