In a large pot, melt 2 tablespoons of unsalted butter over medium heat, allowing it to foam up slightly. Once melted, add 1 finely chopped medium onion and sauté for about 5 minutes until it turns translucent and soft.

Stir in 2 minced garlic cloves into the pot, and sauté for an additional minute while stirring. Be attentive to avoid burning the garlic.

Add 3 peeled and diced medium potatoes and 1 cup of sliced fresh mushrooms to the pot. Stir everything well to ensure that the vegetables are coated.

Pour in 4 cups of vegetable or chicken broth, ensuring all the ingredients are completely submerged. Bring to a gentle boil over medium-high heat while occasionally stirring.

Season the mixture with 1 teaspoon of dried dill, 1 teaspoon of salt, and ½ teaspoon of black pepper, stirring well to combine. Bring the soup back to a gentle boil, then reduce the heat to low.

Cover the pot and allow it to simmer for about 20 minutes, or until the potatoes are tender enough to easily pierce with a fork.

Once the potatoes are tender, carefully use an immersion blender to puree the soup to your desired consistency.

Stir in 1 cup of heavy cream and gently heat the soup until warmed through, being careful not to boil it.

Taste the soup and adjust the seasoning as needed, adding more salt or pepper if desired.

Ladle the warm soup into bowls, garnishing each with freshly chopped parsley.