Preheat oven to 400º. In a large bowl, combine 2 cups mozzarella, Parmesan, garlic, marinara, parsley, and red pepper flakes and season with salt and pepper. Stir until combined, then gently fold in chicken.
Spoon mixture into halved bell peppers and sprinkle with remaining 1 cup mozzarella.
Pour chicken broth into baking dish (to help the peppers steam) and cover with foil.
Bake until peppers are tender, 55 minutes to 1 hour. Uncover and broil 2 minutes.
Garnish with parsley and more Parmesan before serving.
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