To prepare the ragu, place the duck in a bowl and add the paprika, salt and pepper. Stir the duck pieces to coat them evenly with the seasonings.

In a heavy pot, warm the olive oil. Add the duck and sear until golden brown. Transfer to a bowl. Add the mushrooms, onion, carrot and celery to the pot and cook, stirring occasionally, until the onion is translucent. Add the duck and garlic and cook for 1 minute. Add the tomatoes, breaking them up with a spoon, and cook for 4 minutes. Pour in the wine, stirring to scrape up the browned bits, and simmer until the mixture is reduced by half. 

Meanwhile, preheat the oven to 325°F. 

Put the peppercorns, parsley, rosemary and bay leaf on a square of cheesecloth and fold it around the herbs to make a pouch, tying it closed with kitchen string. Add the herb bundle and enough stock to almost cover the meat. Return the mixture to a simmer, cover and transfer to the oven. Cook until the duck falls apart and the sauce is thick, about 2 hours. Season with salt and pepper. Remove and discard the herb bundle.

To make the cavatelli, in a large bowl, mix together both flours, ricotta and eggs and knead the dough with your hands for about 5 minutes. Using a cavatelli maker, roll out the dough 1/4 inch thick and cut it into strips. Run each strip through the cavatelli cutter.

Bring a large pot of salted water to a boil over high heat. Add the cavatelli and cook until tender yet firm, 5 to 6 minutes. Drain the pasta and add it to the ragu, along with the cheese and butter. Stir until the pasta absorbs the sauce and becomes creamy. Adjust the seasoning with salt and pepper and serve.