Soak the dried shitake mushrooms in hot water for 15 minutes while you prepare the other ingredients.
Heat oil in a large pot over a medium heat. Once the oil has melted, add in the fresh mushrooms. Cook for 10 minutes, stirring occasionally, until the mushrooms begin to brown.
In the meantime, strain the soaking mushrooms, BE SURE TO RESERVE THE SOAKING WATER, give them a chop and add into the pot with the sauted mushrooms. Season with salt and pepper.
Add the shallots and garlic to the pan, stirring, and cook for another 2 minutes. Add in the stock and reserved mushroom liquid and bring just to a boil. Turn off the heat and in your half and half.