Preheat the oven to 350 degrees. Melt the 2 Tablespoons butter in a large saucepan over medium heat. Add the diced onions and cook for 5 minutes, until softened.
Add the chicken broth and rice and let simmer. Once simmering, stir, reduce heat and put a lid on it and let cook until rice is cooked (7-8 minutes). Add the broccoli, cover, cook for 8 more minutes.
Add the diced ham, condensed soup, sour cream, milk, and onE cup of the cheddar cheese. Stir until well-combined. Spread into a lightly greased 9 x 13 casserole dish. Top with remaining cheddar cheese. Cover and bake for 25 minutes.
Serve immediately.