Place the diced potatoes, broccoli florets, diced onion, minced garlic, vegetable broth, salt, and black pepper into the slow cooker.
Stir the ingredients once to distribute them evenly, then cover and cook on low for 6 to 7 hours until the potatoes are soft.
Use a potato masher to break down some of the potatoes and broccoli for a thicker texture while leaving some pieces intact.
Add the shredded cheddar cheese and stir until it melts completely into the soup.
Pour in the heavy cream and stir until the soup is smooth and evenly combined. Serve right away.