In a small bowl, soak the dried porcini in 1 cup warm water until soft, about 20 minutes. Remove, squeeze gently, and chop coarsely. Discard water, and set mushrooms aside.
In a large saute pan over medium heat, melt butter with olive oil. Add shallot and garlic, and cook until slightly soft, 2 to 3 minutes.
Add porcini, and saute 1 minute. Add cremini, and cook 1 minute more. Turn up heat to medium high, and add remaining mushrooms. Season with salt and pepper.
Add chopped rosemary, and stir gently until mushrooms are tender, 5 to 7 minutes. Remove pan from heat, and carefully add cognac (you'll have some flames). Return pan to heat, and allow the alcohol to cook off, about 1 minute. Serve hot over creamy polenta.
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