Chicken, broccoli, and mushroom casserole

1 rotisserie chicken, breast and leg meat diced
1/2 lg. onion, diced
1 lb. mushrooms, sliced
1 lb. broccoli, cut into bite-sized florets
8 oz. bok choy, diced
2 Tbsp. butter
2 Tbsp. extra virgin olive oil
2 c. half and half
3 Tbsp. corn starch
4 oz. shredded cheddar
Salt and pepper to taste

Remove the meat from the chicken, dice it into bite-sized cubes, and save the carcass for stock. Cook mushrooms and onions in butter and olive oil until mushrooms have released their water and the onions are translucent. Add the bok choy and cook until the leaves wilt. Meanwhile, steam the broccoli florets. Mix all of the vegetables, any remaining cooking liquid, and chicken in a large bowl. Fold in shredded cheddar. Warm half and half over medium heat. Turn heat to medium-high and whisk in corn starch until thickened. Mix sauce with the vegetable and chicken mixture. Pour into a deep-dish 8x8 casserole and bake 30 mins, or until bubbly.