Rinse the dried white beans and soak them in water overnight. Drain and set aside.
In a large pot, add the salted pork and cover it with cold water. Bring to a boil and then reduce the heat to a simmer. Cook for about 30 minutes to remove excess salt.
Drain the pork and discard the water. Rinse the pork under cold water to remove any remaining salt. Cut the pork into bite-sized pieces.
In the same pot, add the chopped onions, carrots, minced garlic, bay leaves, dried thyme, and the soaked white beans. Add enough water to cover the ingredients.
Bring the pot to a boil and then reduce the heat to a simmer. Cook for about 1.5 to 2 hours until the beans are tender and the pork is cooked through.
Season with salt and pepper to taste.
Serve petit salé hot, garnished with chopped fresh parsley.