With the rack in the middle position, preheat the oven to 180 °C (350 °F).
In a large skillet, brown the roast in half the oil. Season with salt and pepper. Deglaze with the vinegar. Add the honey and shallot. Coat the meat thoroughly.
Add the broth and roast for about 1 hour and 10 minutes or until a thermometer inserted into the centre of the roast reads 82 °C (180 °F). Add broth during cooking, if needed. Cover and let rest for about 15 minutes.
Meanwhile, in a non-stick skillet, brown the apples and garlic in the oil. Season with salt. Pour the apples into the pan juices.
Slice the roast and drizzle with the pan juices and apples. Serve with wilted spinach or steamed bok choy.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.