Step 1: Begin by preparing your vegetables. Wash, peel, and dice the potatoes into small, uniform cubes. If you're using fresh broccoli, cut it into bite-sized florets.
Step 2: In your Crock Pot, combine the diced potatoes, broccoli florets, diced onion, minced garlic, and dried thyme. Pour in the vegetable or chicken broth. Season generously with salt and pepper. Stir all the ingredients together to ensure they are well combined.
Step 3: Place the lid on your Crock Pot and cook on low heat for 6-7 hours, or on high heat for 3-4 hours, until the potatoes are fork-tender and the broccoli is soft.
Step 4: Once the vegetables are tender, it's time to achieve that creamy consistency. Use an immersion blender directly in the Crock Pot to puree the soup to your desired smoothness. If you prefer a soup with some texture, blend only about half of it, leaving some chunks of potato and broccoli.
Step 5: Now for the magic! Stir in the heavy cream and the shredded sharp cheddar cheese. Continue to stir until the cheese is completely melted and the soup is beautifully smooth and creamy. Taste and adjust the seasoning with additional salt and pepper if needed.
Step 6: Ladle the hot soup into bowls. Garnish with your favorite optional toppings, such as a sprinkle of fresh chives, extra cheddar cheese, or a handful of crispy croutons. Serve immediately and enjoy every comforting spoonful!