Preheat the oven to 375 degrees F (190 degrees C).
Heat olive oil in a heavy, oven-safe skillet over high heat. Cook chicken breasts on both sides until golden brown, about 5 minutes per side. Remove chicken breasts from skillet and set aside. Add onion and ground beef to the skillet; cook until onions are starting to brown, about 5 minutes. Add garlic and cook for 1 to 2 minutes. Season with cinnamon, allspice, salt, and cayenne pepper. Cook and stir for 2 minutes.
Stir rice into the skillet until fully coated with oil and spices. Place chicken breasts on top of the rice and pour in broth. Cover skillet with a tight-fitting lid or aluminum foil.
Bake in the preheated oven until rice has absorbed all liquid, about 20 minutes. Remove from oven and sprinkle with parsley before serving.
