Start by peeling and cubing the potatoes. Dice the onion and mince the garlic.
In your crockpot, add the cubed potatoes, broccoli florets, diced onion, and minced garlic.
Pour in the vegetable broth to cover the vegetables. Stir in the salt, black pepper, and dried thyme.
Drizzle the olive oil over the mixture and give it another gentle stir to combine all the ingredients.
Cover the crockpot and cook on low for 6 hours, or until the potatoes are tender.
After 6 hours, once the vegetables are tender, use a blender to puree the soup until you reach your desired consistency.
Stir in the shredded cheddar cheese and milk. Allow it to cook on low for an additional 15-20 minutes, just until the cheese melts completely and the soup is creamy.
Taste and adjust seasoning if necessary before serving.
Serve hot, optionally topped with croutons for added crunch.