Place the chopped onion, minced garlic, diced potatoes, broccoli florets, chicken broth, salt, and black pepper into the crockpot.
Stir once to distribute the ingredients evenly.
Cover and cook on low for 6 hours until the potatoes are soft.
Use a potato masher to break down some of the potatoes and broccoli for thickness while leaving visible chunks.
Stir in the milk, then add the shredded cheddar cheese a handful at a time until fully melted.
Cover and cook on low for 15 more minutes before serving.