Place a large stock pot over high heat. Once hot, place the duck pieces with the fat facing down, fry on both sides until golden brown. Drain the fat into a bowl and keep it. Reduce the heat to medium.
Add in 1 onion cut in quarters (keep the skin on for more stock colour), the carrot, the whole crushed garlic cloves, the bay leaves, and the rosemary and thyme sprigs. Cook for a minute or two. Deglaze with the port or red wine.
Add HALF the chouriço and all the bacon to the stock pot, cover with the water. Season it with salt and black pepper, and let it simmer for 40 minutes.
Remove the duck pieces, the bay leaf and herbs, the bacon and the chouriço from the broth, set aside to cool. Remove the meat from the duck legs.
Add the bones and skin back into the pot and return to the heat and continue to simmer another 20 minutes or so.
As the stock continues to cook, shred up the rest of the duck and set it all aside, discarding any skin or fat. Finely chop the bacon and chourico that was in the pot and set aside.
Once the stock has cooked a little longer, remove from heat and let cool slightly then remove as much fat from the top as you can, then strain the stock. Discard the bones and bits. If you have the time, you can store the stock in the fridge to harden the fat, making it easier to remove.