Cut the bell peppers in half lengthwise and seed them. Blanch them in a large pan of boiling water for 5 minutes, and remove with a slotted spoon. Place upside-down to drain.
Pour the bouillon into another pan, add rice, and bring to a boil. Lower the heat, cover, and simmer for 15 minutes. Remove the pan from the heat and let stand, covered, for 5 minutes.
Meanwhile, heat olive oil in a large skillet. Add the onion and cook, stirring occasionally, for 5 minutes until softened. Add the garlic, mushrooms, tomatoes, and carrot and season to taste with salt and pepper. Cover and cook for another 5 minutes.
Stir the rice, parsley, crumbled goat cheese, and pine nuts into the vegetable mixture. Place the bell pepper halves cut side up in a roasting pan. Divide the rice and vegetable mixture amont them.
Sprinkle the tops of the bell peppers with the grated cheese and bake at 375 degrees for about 20 minutes, until the cheese is brown and melted. Serve immediately.