In a large oven-safe skillet heat oil over medium-high heat. Add onion and cook until soft, about 5 minutes. Add garlic and cook 1 minute more. Add chicken and season with salt and pepper. Cook, stirring occasionally, until chicken is golden on the outside, about 6 minutes.
Stir in rice, heavy cream, and chicken broth. Bring to a simmer over medium low heat, cover and cook until rice is tender (about 30 minutes), stirring occasionally.
When rice is tender, add broccoli, and 1½ cups of the cheddar cheese. Mix until combined and continue simmering until broccoli is tender and cheese is melted, about 5 minutes. Season with more salt and pepper if needed and add more chicken broth if needed. (You want this mixture to be moist and more on the “wet” side.)
Heat broiler.
In a small bowl, mix together the bread crumbs, parmesan cheese and melted butter, set aside. Sprinkle the remaining ½ cup grated cheese over chicken & broccoli followed by the bread crumb mixture. Broil until golden and crispy, about 2 minutes. Serve immediately.