With the rack in the middle position, preheat the oven to 230°C (450°F).
In a large bowl, toss the potatoes with the oil. Season with salt and pepper. Spread the vegetables out on a non-stick or foil-lined baking sheet. Bake for 20 minutes.
Meanwhile, in the same bowl, toss the Brussels sprouts and mushrooms with the leftover oil. Season with salt and pepper. Add more oil as needed. Set aside.
In another bowl, whisk together the mayonnaise, mustard and honey. Season with salt and pepper.
On a plate, using a pastry brush, cover the pork with 2 tbsp (30 ml) of the mayonnaise mixture. Add the vinegar to the bowl of remaining mayonnaise mixture. Cover and refrigerate the sauce until ready to serve.
Remove the baking sheet from the oven. Add the Brussels sprouts and mushrooms. Stir the vegetables and push them towards the sides of the baking sheet. Place the pork at the centre of the baking sheet. Bake for 15 minutes or until a thermometer inserted in the centre of the pork reads 71°C (160°F). Brown the meat under the broiler, if desired. Remove from the oven. Let rest for 5 minutes before serving.
On a work surface, slice the pork tenderloins. Divide the vegetables and meat among six plates. Serve with the mayonnaise sauce.