In a large pot, melt butter and sauté onion until soft. Add garlic and cook 1 minute until fragrant.
Stir in diced potatoes and pour in broth. Simmer on medium heat for 20 minutes, or until potatoes are tender.
Use an immersion blender to partially blend the soup, leaving some chunks for texture.
Reduce heat to low. Stir in heavy cream, shredded cheddar, thyme, salt, and pepper. Mix until cheese is fully melted and soup is creamy.
Garnish with parsley and optional toppings. Serve hot with bread or salad.
Slow Cooker Version:
Add onions, garlic, potatoes, broth, salt, pepper, and thyme to slow cooker. Cook on low for 6–7 hours or high for 3–4 hours. Stir in cream and cheddar at the end, then garnish before serving.