Preheat the oven to 400 degrees. Slice the tops off the garlic heads, drizzle with olive oil, and wrap in foil. Roast for 35 minutes until the cloves are soft and golden.
Add the roasted garlic cloves, broccoli florets, diced onion, vegetable broth, and dried thyme to the slow cooker.
Cover and cook on low for 6 hours or on high for 3 hours until the broccoli is very tender.
Use an immersion blender to puree the soup until smooth, or transfer to a blender in batches.
Stir in the shredded cheddar cheese until fully melted, then add the heavy cream.
Season with salt and black pepper. Serve hot.