Place the broccoli florets, diced smoked ham, diced onion, minced garlic, chicken broth, salt, and black pepper into the slow cooker. Stir to combine.
Cover and cook on low for 5 hours until the broccoli is tender.
Melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for 1 minute to form a roux.
Slowly whisk the milk into the roux and continue stirring until the mixture thickens slightly, about 2 minutes.
Pour the milk mixture into the slow cooker and stir well to combine.
Add the shredded cheddar cheese a handful at a time, stirring until fully melted and the soup is smooth.