With the rack in the middle position, preheat the oven to 350°F (180°C).
In a large Dutch oven or ovenproof pot over medium-high heat, brown the meat in 2 tbsp of the butter. Season with salt and pepper. Remove and set aside on a plate.
In the same pot, brown the onions in the remaining butter. Add the garlic and cook for 1 minute. Deglaze the pot with the broth and vinegar. Add the meat. Bring to a boil, cover and bake for 2 hours or until the meat is fork tender. Remove from the oven. Remove any excess fat from the meat, shred and combine with the warm sauce. Set aside.
Meanwhile, prick the potatoes in several places with the tip of a knife and place directly on the oven rack. Bake for 1 hour (along with the pork) or until very tender. Remove from the oven.
Peel the potatoes immediately and purée with a potato ricer or potato masher to obtain 1 ½ cups (375 ml) of mashed potatoes. Set aside in a bowl. Season with salt.
Add the egg and ½ cup (75 g) of the flour to the mashed potatoes. Mix thoroughly by hand. Stir in the remaining flour and knead the warm dough on a floured work surface until soft and smooth. Add more flour, if needed.
Divide the dough into four pieces. Form four logs, each ¾ inch (1.5 cm) thick. Immediately cut each roll into ¾-inch (1.5 cm) pieces. Sprinkle lightly with flour. Roll the dough pieces on the tines of a fork to give them a rounded shape and a striped pattern. Place the gnocchi on a lightly floured baking sheet.
In a large pot of salted boiling water, cook the gnocchi for 2 to 3 minutes or until they rise to the surface of the water. Drain and toss with the warm pork and sauce. Add the parsley. Adjust the seasoning.
You can make the gnocchi a few hours before cooking them; just keep them in the refrigerator on a lightly floured baking sheet or plate.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.