Melt butter in a skillet over medium heat. Sauté diced onions until translucent.
Sprinkle flour over the onions and stir to create a roux. Cook until it turns light golden brown.
Transfer the onion mixture to the crockpot.
Add broccoli florets and chicken/vegetable broth. Season with salt, pepper, and nutmeg. Stir gently.
Cover and cook on LOW for 4-5 hours or until the broccoli is tender.
Use an immersion blender to blend the soup until smooth. Alternatively, transfer to a regular blender in batches, taking care with hot liquid.
Return the soup to the crockpot and stir in shredded cheddar cheese until melted and creamy.
Pour in whole milk and let it warm through for about 10-15 minutes on LOW heat.
Taste and adjust seasoning if necessary.
Ladle the soup into hollowed-out bread bowls.