In a large pot, melt the butter over medium heat. Add the diced onion and sauté for about 5 minutes, until softened. Stir in the minced garlic and cook for an additional minute until fragrant.

Add the diced potatoes to the pot and pour in the vegetable broth. Bring the mixture to a boil, then reduce the heat and simmer for about 20 minutes, or until the potatoes are tender.

Once the potatoes are cooked, use an immersion blender to puree the soup until smooth. If you prefer a chunkier texture, blend only half of the soup and leave the rest as is.

Stir in the heavy cream and dried dill. Season with salt and pepper to taste. Heat the soup over low heat until warmed through, but do not boil.

Serve hot, garnished with chopped fresh dill.