Add the broccoli florets, diced onion, minced garlic, vegetable broth, salt, and black pepper to the slow cooker. Stir once to combine.
Cover and cook on low for 4 hours or on high for 2 hours until the broccoli is very tender.
In a small bowl, whisk the flour into the milk until smooth. Pour the mixture into the slow cooker and stir well.
Cover and cook on high for 20 more minutes to thicken the soup.
Turn off the heat. Add the shredded cheddar cheese a handful at a time, stirring until fully melted and smooth before adding the next handful.