Heat a large, heavy-bottomed soup pot over medium heat. Add the chicken stock to start warming.
Add your dried porcini mushrooms to a glass bowl. Pour 1.5 to 2 cups of very hot water over them. Allow them to soak for 15 minutes. After they have rehydrated, strain them through a sieve lined with a paper towel or cheesecloth. Add the mushroom stock to the chicken stock and rinse the remaining porcini under cold water to remove any grit. Set the porcini aside.
In a large sauté pan, add in 2 tablespoons of butter and olive oil. Heat over high heat. Add the onions, leeks, and shallots. Add a pinch of salt. Cook for 2-3 minutes, stirring frequently.
After 2 or 3 minutes, add in the garlic and thyme. Continue cooking for another 3-4 minutes or until very fragrant and the leeks lightly brown. Add the onion mixture to the hot broth.
Add the remaining butter and olive oil. Return the pan to high heat and add in the fresh mushroom mixture. If you need to split your mushrooms into 2 batches, make sure that you split the butter and olive oil as well. Cook the mushrooms for 3 minutes and then add a couple of pinches of salt. Cook for 2 more minutes and add to the chicken stock when nicely browned.
If none remains from the last batch of mushrooms, add a touch of oil to the pan. Add the rehydrated porcini. Cook for 3-4 minutes or until very fragrant. Add the chicken stock.
Bring the soup to a boil. After the soup boils for 1-2 minutes, reduce to a simmer and cook for 15 minutes. Add in the balsamic vinegar. Taste the soup and adjust the seasoning. Add the remaining salt and pepper sparingly, remembering to stir, taste, and readjust until it is balanced.
Turn off the heat and remove about ¼ of the soup from the pot. Make sure that you have a lot of the mushrooms in the bowl that is set aside. Add the parsley and sour cream to the soup remaining in the pot. Purée the soup with your immersion blender. Taste and adjust the seasonings.
Add the set-aside chunky soup back into the puréed soup. Mix well. Serve hot and enjoy!