Add the chicken broth, diced onion, and minced garlic to the slow cooker and stir to combine.
Cover and cook on low for 2 hours to allow the flavors to develop.
In a small bowl, whisk together the flour and half-and-half until smooth, then pour into the slow cooker along with the cubed cream cheese.
Add the broccoli florets, salt, pepper, and nutmeg, then stir well to combine.
Cover and cook on low for an additional 2 hours, until the broccoli is tender and the soup has thickened.
Stir in the shredded cheddar cheese until completely melted and smooth, then serve hot with extra cheese on top if desired.