Season the pork shoulder pieces with salt and black pepper.
Place the pork, garlic, shallots, thyme, bay leaves, and white wine into a Dutch oven.
Cover and cook at 275°F (135°C) for 3-4 hours, until the pork is fork-tender.
Remove the bay leaves and thyme stems, then shred the pork with a fork.
Mix in the melted pork fat until the texture is smooth and spreadable.
Transfer the rillettes to a jar, press down to remove air pockets, and seal with a thin layer of melted fat.
Chill for at least 24 hours before serving with bread and pickles.