Place the dried mushrooms in a pyrex measuring cup and pour on 2 cups boiling water. Let soak 30 minutes, while you prepare the other ingredients. Place a strainer over a bowl, line it with cheesecloth or paper towels, and drain the mushrooms. Squeeze the mushrooms over the strainer to extract all the flavorful juices. Then rinse the mushrooms, away from the bowl with the soaking liquid, until they are free of sand. Squeeze dry and set aside. If very large, chop coarsely. Measure out 1 1/2 cups of the soaking liquid and set aside.

Heat the olive oil in a large, heavy, nonstick skillet over medium heat and add the onion. Cook, stirring often, until tender, about 5 minutes. Add half the garlic, stir together for about 30 seconds, then add the mushrooms and about a teaspoon of salt. Cook, stirring often, until the mushrooms begin to soften and to sweat, about 5 minutes. Add the flour and continue to cook the mushrooms, stirring, until they have softened a little more and you can no longer see the flour, about 2 minutes. Add the reconstituted dried mushrooms, the soy sauce and the wine and turn the heat to high. Cook, stirring, until the liquid boils down and glazes the mushrooms, 5 to 10 minutes. Add the rosemary and sage, stir together, and stir in the mushroom soaking liquid. Bring to a simmer, add salt to taste, and cook over medium-high heat, stirring often, until the mixture the mushrooms are thoroughly tender and fragrant and the surrounding broth is thick and gravy-like, about 10 to 15 minutes. Remove from the heat, stir in some freshly ground pepper, taste and adjust salt. Set aside, preferably in the refrigerator, overnight.

*Advance preparation: The ragout can be made up to 3 or 4 days before you wish to serve it, either on its own or in the cobbler.

Oil or butter a 2-quart gratin or baking dish. Preheat the oven to 375 degrees F. Check mushroom seasonings one more time and adjust if necessary. Transfer to the prepared baking dish. Make the cobbler topping. Sift together the flours, baking powder, baking soda, and salt. Cut in the butter, with forks, your hands or in a food processor fitted with the steel blade. Stir together the yogurt and the smaller amount of milk, and add to the flour mixture. If it seems dry add the remaining milk as needed. Gather gently into a ball, then press or roll out to fit the baking dish, and cover the mushrooms; alternatively, drop by spoonfuls over the mushrooms. Slash in a few places with a sharp knife. Brush the top with beaten egg, then bake until golden, about 30 to 40 minutes.

*Advance preparation: The mushroom ragout can be made up to 4 days before assembling and baking the cobbler. The biscuit topping can be mixed up, shaped into a 1-inch thick round, wrapped in plastic and refrigerated overnight. The assembled cobbler can sit in the refrigerator for a few hours before baking.

Keeping time / Leftovers
The ragoût will be good for 5 days in the refrigerator. The cobbler will do fine as a leftover for a couple of days. Reheat in a low oven or microwave.