Preheat oven to 375 degrees F.
Cut the bell peppers in half lengthwise and remove the ribs and seeds. Place the peppers, cut sides up, in a baking dish. (You may need two baking dishes to fit them all.) Set aside.
Place the quinoa and water in a small saucepan. Bring to a boil and then reduce the heat to a low simmer. Cover and simmer until all of the liquid has been absorbed, about 15 minutes.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the onions, carrot, and celery and cook, stirring occasionally, until the vegetables begin to soften, about 3 minutes. Add the mushrooms and cook until they begin to soften and brown, about 5 minutes. Add the garlic and cook, stirring, for 30 seconds. Remove from the heat.
Pour the marinara sauce into the skillet with the vegetables and stir to combine.
Add the beans, cooked quinoa, parsley, and ¾ cup of the mozzarella to the skillet, and stir until evenly combined. Season with salt and pepper to taste.
Scoop the filling into each of the bell pepper halves, and top with the remaining mozzarella cheese. Cover baking dish with foil and bake for 35 minutes, until the peppers have slightly softened and the filling is hot. Uncover and bake for 5 more minutes, until the cheese just begins to brown. Let stand for about 5 minutes before serving.