Melt butter and olive oil together in a large frying pan over medium heat. Cook and stir potatoes, chicken, onion, green bell pepper, chicken broth, steak seasoning, garlic powder, and seasoned salt in the hot butter-oil mixture until chicken is no longer pink in the center and liquid is evaporated, 15 to 20 minutes. Add more olive oil if mixture becomes dry.

Stir broccolini and Cheddar cheese into chicken hash; cook until broccolini are tender and Cheddar cheese is melted, 2 to 3 more minutes.