Place the broccoli florets, diced onion, chicken broth, butter, garlic powder, salt, and black pepper into the slow cooker.
Stir once to combine everything evenly.
Cover and cook on low for 5 hours until the broccoli is very tender.
Stir in the shredded cheddar cheese and half-and-half.
Cover again and cook on low for 30 more minutes, stirring once halfway through, until the cheese melts completely and the soup thickens.