With the rack in the middle position, preheat the oven to 150°C (300°F).
In a bowl, combine the mustard, honey and garlic. Set aside.
In a large ovenproof saucepan or Dutch oven over medium-high heat, brown the pork on all sides in 30 ml (2 tablespoons) oil. Season with salt and pepper. Remove from the pan and brush with the mustard mixture. Set aside on a plate.
In the same pan over medium-high heat, brown the onion and apples for about 2 minutes, adding oil as needed. Deglaze with the vinegar. Return the pork to the pan and add the apple juice. Cook uncovered in the oven for 2 hours, 45 minutes, basting 5 or 6 times during cooking. Add apple juice or chicken broth as needed.
In a skillet over medium-high heat, fry the sausage slices in the remaining oil. Add to the braise and continue cooking for 30 minutes. Adjust the seasoning.
Serve with mashed potatoes.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.