1. Separate all mushroom stems and caps, and set caps aside. Coarsely chop mushroom stems, then simmer in chicken stock, covered, for one hour. Strain mushroom stems from chicken broth. Reserve the broth and discard stems. Return broth to pot and set aside.
2. In the meantime, cut mushroom caps into a half-inch dice. Heat oil in a large skillet, and sauté shallots and garlic until softened, about three minutes. Add thyme, rosemary, salt, and pepper and cook for two minutes.
3. Add diced mushrooms and reduce heat to low. Cook gently until most of the liquid is released and evaporated. If using fresh herbs, remove thyme and rosemary sprigs.
4. Raise heat and add Cognac. Cook until alcohol is mostly reduced and mushrooms start to turn a little golden on the edges.
5. Add mushroom and shallot mixture to the strained broth and heat gently.
6. Add creamer and chives. Serve warm, topped with frizzled onions if desired.