1⁄2 cup roughly chopped parsley, plus 2 tbsp. finely chopped
2 tbsp. rosemary leaves
3 large sage leaves
2 cloves garlic, peeled
2 stalks celery, roughly chopped
1 small yellow onion, roughly chopped
1⁄4 cup olive oil
2 lb. whole duck legs
Kosher salt and freshly ground black pepper, to taste
1⁄2 cup dry white wine
6 oz. fresh or dried pappardelle
1⁄2 cup grated parmesan
Bring 1 cup stock to a boil in a 1-qt. saucepan; add porcini mushrooms, remove from heat, and let soak until soft, about 30 minutes. Using a slotted spoon, transfer mushrooms to a colander and squeeze dry; roughly chop and set aside. Pour soaking liquid through a fine-mesh strainer, discarding gritty sediment in pan; set aside.
Purée 1⁄2 cup roughly chopped parsley, plus rosemary, sage, garlic, celery, and onion in a food processor until smooth; set aside. Heat 2 tbsp. oil in a 12" skillet over medium-high heat. Season duck with salt and pepper; cook, flipping once, until browned, 4–6 minutes. Transfer duck to a plate; set aside. Pour off all but 1⁄4 cup fat from pan, reserving remaining fat for another use; return pan to medium-high heat. Add vegetable purée; cook, stirring occasionally, until golden and slightly dry, 2–4 minutes. Add reserved mushrooms and duck to pan and increase heat to high. Add wine; cook, until almost completely reduced, about 5 minutes. Add reserved soaking liquid and remaining stock; bring to a boil. Reduce heat to low; cook, covered, until duck is tender when pierced with a knife, 1 1⁄2–2 hours. Using tongs, transfer duck to a cutting board; set aside until cool enough to handle, then shred meat, discarding skin and bones. Add meat to sauce and return to a simmer; cook until sauce is slightly thick, 10–12 minutes.
Bring a large pot of salted water to a boil. Cook pasta until al dente, about 3 minutes if using fresh. Drain pasta; add to skillet. Add half the parmesan, plus salt and pepper; toss to combine. Transfer pasta to a serving dish; garnish with finely chopped parsley and remaining parmesan.