Step 1Cover the dried mushrooms with the warm water; set aside to soften, about 10 minutes.
Step 2In a food processor with the motor running, drop the shallot through the feed tube and chop until finely minced, 10 seconds. Scrape down the sides of the work bowl, add the white mushrooms and the lemon zest and pulse to mince them as well. Drain the dried mushrooms and squeeze dry, reserving the liquid to add to stock or soup. Add the softened mushrooms to the food processor; pulse to mince.
Step 3Melt the butter in a large skillet over medium-high heat. When the butter is sizzling, add the minced mushroom mixture. The mushrooms will almost instantly absorb all of the butter. Let them continue to cook, stirring frequently, and after 2 or 3 minutes, they will begin to release their moisture. Season with 1 teaspoon of salt, thyme, rosemary and a generous grinding of pepper and continue cooking until the moisture from the mushrooms has been reabsorbed and the bottom of the pan is completely dry when you drag a spoon across it, about 5 minutes. Add the Cognac and lemon juice and cook until the mushrooms are completely dry again, about 2 minutes. Remove from the heat and cool. (The recipe can be prepared to this point as much as a day ahead and refrigerated, tightly sealed.)
Step 4Heat the oven to 400 degrees. Rinse the chicken inside and out with cold water and pat dry. Using your fingers, separate the skin covering the breast from the meat at the main cavity. Work your hand way underneath the skin until you have completely separated it from the breast meat up to the wishbone.
Step 5Carefully spoon the mushroom mixture into the pocket between the skin and the meat. As you work, press the skin with your hand to push the mushrooms all the way to the wishbone end of the breast. The mushrooms should completely cover the breast, forming a layer about 1/2- to 3/4-inch thick.
Step 6Truss the chicken: Cut a piece of kitchen twine 18 to 24 inches long. In the center of the twine, form a loop and wrap it around the knob of one drumstick. Pull the other drumstick tightly alongside, secure it with another loop and pull it tight. Take the 2 loose ends of the twine and wrap them snugly around the outside of the chicken so that they holdthe wing tips to the breast meat. The twine should not be so tight it cuts into the meat. Tie off the ends and cut any excess twine.
Step 7Generously salt and pepper the outside of the chicken and place it breast-side up on a rack in a low-sided roasting pan. Roast until a thermometer inserted in the deepest part of the thigh registers 160 degrees, 70 to 80 minutes. Remove the chicken from the oven and cover loosely with foil. Set aside for 10 minutes before carving. Carve as you would a turkey.