In a large pot, set over medium heat, combine the olive oil, chicken, and onion. Cook until fragrant, about 5 minutes. Season with salt and pepper. Add the butter, thyme, paprika, and garlic powder. Mix in the rice and pasta, cook until golden and toasted, 2-3 minutes. Add the broth and bring to a boil over high heat. Add the broccoli and a large pinch each of salt and pepper. Bring to a boil, cover, and reduce the heat to low. Cook, covered for 20-25 minutes, until the rice is mostly cooked.Once the rice is cooked, stir in the milk. Add the cheese, then remove from the heat. Stir until creamy. Serve warm with additional thyme and black pepper.