Preheat the oven to 350℉. Lightly grease a baking dish and set it aside.
Wash the bell peppers, slice off the tops, and remove the seeds and membranes. Set the peppers and tops aside.
Cook the rice in boiling water for 7-10 minutes until slightly undercooked. Drain well and set aside.
Heat the olive oil in a large skillet over medium heat. Add the onion, carrot, mushrooms, and garlic, and cook for 3-4 minutes until softened. Add the chopped chicken thighs to the skillet and cook until the chicken is no longer pink, about 5-6 minutes.
Stir in the paprika, cumin, salt, and black pepper, mixing well to evenly coat the filling.
Remove the skillet from the heat and transfer the mixture to a large bowl. Add the partially cooked rice and mix until fully combined. Adjust seasoning if needed.
Spoon the chicken and rice mixture into each bell pepper, pressing gently to fill. Place the pepper tops back on.
Arrange the stuffed peppers upright in the prepared baking dish. Pour the water or tomato juice into the bottom of the dish. Cover tightly with foil and bake for 30 minutes.
Remove the foil and bake for an additional 10 minutes, until the peppers are tender and the tops are lightly browned. Remove from the oven and rest for 5 minutes before serving.