How to Make It
Preheat the oven to 325°. In a small bowl, soak the dried porcini in 1 cup of the boiling water until the porcini are softened, about 20 minutes. Using your fingers, rub any grit off the mushrooms in the soaking liquid. Drain the mushrooms, reserving the soaking liquid; squeeze any excess liquid from the mushrooms and coarsely chop them. Slowly pour the mushroom soaking liquid into a cup, stopping before you reach the grit at the bottom.
In a medium bowl, soak the pearl onions in the remaining 1 cup of boiling water for 1 minute. Drain the pearl onions, then trim and peel them.
In a large, enameled cast-iron skillet or medium casserole, heat the olive oil until shimmering. Season the duck legs with salt and pepper. Add the duck legs to the skillet and cook over moderate heat until deeply browned, about 5 minutes per side. Transfer the duck legs to a plate. Add the pearl onions to the skillet and cook over low heat, stirring once or twice, until the onions are richly browned all over, about 10 minutes. Transfer the onions to a plate.
Pour off all but 1 tablespoon of fat from the skillet and add the pancetta. Cook over low heat, stirring, until the pancetta is lightly browned, about 4 minutes. Add the shallots, garlic and chanterelles to the skillet and cook, stirring occasionally, until the chanterelles soften, about 5 minutes. Add the potatoes, thyme, chicken stock, wine and the reserved porcinis and porcini liquid and bring to a simmer. Submerge the duck legs in the sauce, cover and bake for 1 hour. Stir in the pearl onions, then cover and bake for 30 minutes longer, or until the duck is very tender.
Using a large spoon, skim the fat from the sauce and discard the thyme sprigs. Season the sauce with salt and pepper. Serve the braised duck hot.