Pre-heat a large Dutch oven over medium heat for about 5 minutes.
If using duck fat, add it to the Dutch oven to melt and heat through. If not using duck fat, don't add any additional fat.
Turn the heat to high and add the salt pork and pork shoulder Brown the meat, stirring occasionally, until browned all over, about 9 minutes .
Using a slotted spoon, transfer to a large bowl, leaving rendered fat in the Dutch oven. Set the browned meat aside.
Season the chicken or duck thighs with pepper (do not add salt) and place skin side down in the Dutch oven.
Cook without moving until well-browned, 6 to 8 minutes.
Transfer to a plate and let cool to room temperature.
Add the sausages to the Dutch oven and cook, turning occasionally, until well-browned, about 2 minutes per side. Transfer to the bowl with the salt pork.
After the chicken or duck has cooled, cover and transfer to the refrigerator.