Add the vegetable broth, chopped broccoli, diced onion, and minced garlic to the slow cooker. Cover and cook on low for 6-8 hours or until the broccoli is very tender and infused with aroma.
Use an immersion blender directly in the slow cooker to blend the soup until it reaches your desired consistency—either smooth or with some chunks for texture.
Stir in the heavy cream and shredded cheese, then continue to cook on low for another 15 minutes to allow the cheese to melt and the flavors to meld.
Season the soup with salt and pepper to taste. Adjust the seasoning, adding a pinch more salt or pepper if needed, and stir well.
Once well seasoned and heated through, serve the soup hot with a sprinkle of additional cheese or fresh herbs if desired, and enjoy its creamy, earthy aroma.