Soak the mushrooms in 1 cup hot water, 10 minutes. Pulse the pancetta, onion, carrot, celery, thyme and sage in a food processor to make a chunky paste.
Pat the duck legs dry and season with salt. Heat the olive oil in a large Dutch oven or pot over medium-high heat. Add the duck legs, skin-side down, and cook until brown on both sides, about 7 minutes per side. Transfer the duck legs to a plate and pour off all but a thin layer of oil from the pot.
Drain the mushrooms, reserving the soaking liquid, then finely chop. Add the pancetta paste to the pot, season with salt and cook, stirring, until the paste is dry and sticks to the pot, 5 to 7 minutes. Clear a space in the pot and add the tomato paste; cook, stirring, 1 to 2 minutes, then add the bay leaves and mushrooms and stir all the ingredients together.
Add the wine and bring to a boil, scraping up any browned bits with a wooden spoon. Cook until the wine thickens, 2 to 3 minutes. Return the duck legs to the pot along with 4 cups water and the reserved mushroom soaking liquid. Bring to a simmer, then reduce the heat to low, cover and cook until the duck is tender, about 1 hour, 20 minutes. Transfer the duck legs to a plate to cool. Skim the fat from the cooking liquid and discard; bring the remaining liquid to a boil and cook until reduced to about 3 cups, about 12 minutes. Discard the skin and bones from the duck; shred the meat and add it to the reduced sauce.
Bring a large pot of salted water to a boil. Return the ragu to a simmer. Add the pasta to the boiling water and cook until al dente, about 2 minutes. Remove with a slotted spoon or skimmer and add directly to the ragu, tossing to coat the pasta with the sauce. Drizzle with olive oil and toss again. Remove from the heat, sprinkle with the parsley and parmesan, and toss.