In a skillet, heat olive oil over medium heat. Add the chopped onion and minced garlic, sautéing until the onion is translucent, about 4-5 minutes.
Transfer the sautéed onion and garlic to the crockpot.
Add the diced potatoes and broccoli florets to the crockpot.
Pour in the vegetable broth and sprinkle the dried thyme, salt, and pepper over the top. Stir gently to combine the ingredients.
Cover and cook on low for 6-8 hours or on high for 3-4 hours, until the potatoes are tender.
Once cooked, use an immersion blender to puree the soup to your desired consistency (smooth or chunky). Alternatively, you can carefully transfer it to a blender in batches.
Return the pureed soup to the crockpot, stir in the milk and shredded cheese, and let cook on low for an additional 30 minutes until the cheese is melted and creamy.
Taste and adjust seasoning if necessary.
Notes
Serve hot with croutons and fresh parsley for garnish.