In a large heavy pot or dutch oven, heat a 1/4 cup olive oil on medium to medium high heat.
Add the pieces of duck, skin side down and cook until browned on the first side, roughly 2 to 3 minutes.
Turn the duck pieces over and brown for another 2 minutes.
Remove the duck pieces and place them on a plate.
Add the onions to the dutch oven and sauté for about 1 minute.
Add the garlic and continue to sauté for another minute or until the onions are soft.
Cook the wine for about 2 minutes.
Place the pieces of duck back in the pot.
Add the chouriço, toucinho, carrots, bay leaf and water.
Bring to a boil and place the lid on the pot.
Reduce the heat to low, and simmer for about 50 minutes.
Place/fit a bowl under the sieve, fill it with water until the rice is submersed, and let the rice continue to soak until it’s needed later in the recipe.
Once the duck is cooked, use tongs to remove the duck pieces, toucinho and chouriço from the broth onto a plate and let cool.
Strain the broth from the pot into a large measuring cup or bowl.
In a medium or large pot, heat 4 1/2 cups of the strained broth until it starts to bubble.
Add the rice, bring to a light boil, reduce the heat to low, cover and let cook for 8 to 9 minutes.
Preheat the oven on the broiler setting.
Once the rice is cooked, remove it from the heat and let it rest covered for about 10 minutes. Don’t peak!
Once the duck has cooled down, shred/pull all the meat off the bones, and discard the bones. Set aside.
Cut the chouriço into wheels and the toucinho in small bite-sized peices.
In a large bowl, place the fluffed rice, shredded duck, 1/2 the chouriço wheels, toucinho pieces, black olives, and toss to mix all the ingredients well.
Place the mixed duck ingredients in a large deep baking dish (we used a traditional red Portuguese clay dish).
Place the dish in the oven and cook for about 5 minutes or until the chouriço edges get a little crispy.
Remove from the oven, garnish with fresh chopped parsley and serve. Enjoy!
Save any leftover broth for future use. Add some of the broth to the rice before reheating the next day to increase the moisture.