Heat the oil in a wide, heavy pot over medium heat. Add the onions and cook, stirring occasionally, until deeply golden, 10 to 15 minutes.
Add the chicken and cook until lightly browned on all sides, about 5 minutes.
Stir in the carrot, salt, pepper, paprika, turmeric and chicken bouillon, and cook until fragrant, 2 to 3 minutes.
Add the rice, cilantro and dill, and stir well to coat.
Pour in the boiling water and bring to a simmer. Cover, reduce heat to low and cook until the rice is tender and the liquid absorbed, 35 to 40 minutes.
Remove from heat and let sit, covered, for 5 to 10 minutes. Fluff gently and serve.