Heat oil in a sturdy pot or deep frying pan. Season duck with salt and pepper. Place them skin side down in the pot and sear until browned and crisp. Turn to brown on the other side.
Transfer the duck to a deep pot or Dutch oven. Then drain all but about 1 tablespoon of the fat from the pan.
On a medium-low heat, add celery, onion, and carrot to the pan. Stir occasionally until softened, which usually takes around 10 minutes. Mix in garlic and cook for an additional minute.
Pour in wine, set heat to high, and let it reduce by half.
Add broth, tomato concentrate, sage, rosemary, and bay leaf. Mix well and bring the sauce to a boil.
Pour the sauce into the pot with the duck. Cover and let simmer until meat is tender, around 1.5 to 2 hours. If sauce thickens too much, add wine or broth as needed.
Once done, remove the duck and set it aside. Skim off excess fat from the sauce. If the sauce is too thin, simmer it until it reaches your desired consistency.
When the duck has cooled enough to be shredded, discard its skin. Detach meat from bones and shred or cut it into small pieces.
Add the meat back to the sauce and let it simmer for 10 minutes. Remove the bay leaf. Season with salt and pepper as needed.
For serving, boil a pot of water. Add salt then the pasta and cook until al dente as per package instructions (or 6-8 minutes if homemade bigoli). Before draining, set aside a cup of pasta water.
Toss the cooked pasta with the duck ragù. If needed, add some pasta water to adjust consistency.
Serve with additional duck ragù on top, garnished with Parmigiano Reggiano.