Start by cubing the giant puffball mushrooms, dicing the onion, and chopping the garlic.
In a large pot, melt 3 tbsp of butter over medium heat. Add the cubed puffball mushroom, diced onion, and garlic. Sauté until the mushrooms begin to brown. The mushrooms will shrink as they cook, so don’t be alarmed by their initial volume. Stir to avoid burning, about 8-10 minutes.
Once the vegetables are soft and browned, sprinkle 2 tbsp of flour over the mixture. Stir it in until the flour is fully combined, forming a thick, paste-like consistency. This will help thicken your soup.
Slowly pour in the beef or chicken broth while stirring constantly. Continue cooking over medium-low heat, stirring frequently to prevent lumps. The soup will begin to thicken as it heats. This will only take a few minutes.
Add 1 cup of milk, and mix in the salt, pepper, thyme, and dill. If you’re using sour cream, stir it in at this stage for extra creaminess. Let the soup return to a gentle simmer to heat everything through, about 5 minutes.
Give the soup a taste and adjust the seasoning if needed. Add more salt, pepper, or herbs to suit your preference.