In a heatproof bowl, pour the hot water over the porcini mushrooms and soak for 30 minutes.
In a large, wide-bottomed saucepan over high heat, warm 2 Tbs. of the oil and melt the butter. Add the button and shiitake mushrooms and sauté, stirring occasionally, until the mushrooms are golden and tender and the liquid has nearly evaporated, 6 to 8 minutes. Add the remaining 1 Tbs. oil to the pan with the mushrooms, then add the onion and garlic. Sauté, stirring occasionally, until the onions are tender and golden, 6 to 8 minutes more. Add the thyme and sauté 1 minute more.
Strain the porcini through a fine-mesh sieve, reserving the soaking liquid and the porcini. Add the soaking liquid to the mushroom-onion mixture along with the vinegar, stock and cream. Bring to a simmer, reduce the heat to medium-low and simmer for 20 minutes.
Using a stick blender, puree the soup until smooth and blended. Season with salt and pepper. Chop the porcini coarsely and stir into the soup. Ladle into warmed soup bowls and garnish each serving with a pinch of chopped chives. Serves 8.