Wash the duck and remove all fat, then pat dry.
In a heavy-bottomed casserole or Dutch oven, heat the olive oil until smoking. Add the goose and cook until brown on all sides— about 10 to 12 minutes— then remove. Add the onion, carrot, garlic and celery and cook until softened, 7 to 9 minutes. Add the wine, tomatoes, and chicken stock then bring to a boil. Add the goose legs and return to a boil. Then lower the heat, cover and allow to simmer for 1 hour. Remove the goose legs and allow to cool. When it’s cool, pull all meat off the bones and return to the pot, without the bones. Simmer uncovered for 30 minutes, or until quite thick. Season with salt and pepper and set aside.
Fill a large pot with 6 quarts of water and add 2 tablespoons salt. Cook paccheri until al dente, about 8 to 9 minutes. Heat the sauce, drain pasta and toss in pan. Toss to coat and serve immediately.