With one rack in the middle position and a second rack in the lowest position, preheat the oven to 400°F (200°C).
In a bowl, combine the mayonnaise, mustard, lemon juice, salt and garlic.
With your fingers, gently detach the skin from the breast and legs of the chicken, being careful not to rip it. Evenly spread half of the mayonnaise mixture under the skin. Spread the remaining mixture all over the outside of the chicken. Attach the chicken legs with butcher’s twine and tuck the wings under the back of the chicken. Place the chicken, breast-side up, in a 13 x 9-inch (33 x 23 cm) glass baking dish. Let marinate for 15 minutes.
Bake on the middle rack of the oven for about 1 hour 45 minutes or until a thermometer inserted in the thigh, without touching bone, reads 180°F (82°C). Set the chicken aside on a plate while you prepare the sauce. Remove any excess fat from the cooking juices and set both aside for the sauce (see note).
Meanwhile, cut the potatoes in half lengthwise. Using a very sharp knife, cut a crosshatch pattern into the cut side of the potatoes, keeping the incisions close together and about ¼ inch (5 mm) deep.
On a baking sheet lined with parchment paper, toss the potatoes with the oil. Arrange the potatoes, cut side down, on the baking sheet. Bake on the lower rack of the oven for 45 minutes or until golden. Turn the potatoes over. Season with salt and pepper. Bake for another 15 minutes or until crispy on the outside and soft at the centre.
In a large skillet over medium-high heat, brown the shallots in the reserved chicken fat. Sprinkle with the flour and cook for 1 minute while stirring. Deglaze with the wine and cook for 1 minute. Add the broth and pepper. Bring to a boil, stirring constantly. Add the reserved chicken cooking juices and let reduce until you have about 1 ¼ cups (310) of sauce. Adjust the seasoning.
Serve the chicken with the potatoes and sauce (see note). Serve with our green bean and red cabbage salad (see recipe), if desired.
If no cooking juices have accumulated in the baking dish, add ⅓ cup (75 ml) water to loosen the brown bits at the bottom of the dish and add to the sauce.