Melt butter in a large pot over medium heat. Add diced onion and sauté for about 5 minutes until translucent, then add minced garlic and cook for another minute until fragrant.

Stir in diced potatoes and pour in chicken or vegetable broth. Increase heat to medium-high and bring to a boil for about 5 minutes.

Reduce heat to medium-low, cover, and let simmer for 15-20 minutes until potatoes are fork-tender.

Blend some of the mixture with an immersion blender for a creamier consistency, or mash for a chunkier texture.

Stir in heavy cream and shredded cheese until cheese melts completely. Adjust seasoning with thyme, salt, and pepper.

Ladle soup into bowls and garnish with herbs or cheese if desired.