Place a dripping pan or aluminum foil dish below the grill on which you will cook the duck to collect the cooking fat and prevent flare-ups. Preheat the barbecue to medium heat, turning off the middle burner to allow indirect cooking.
Trim the excess fat from the end of each breast, score the skin being careful not to cut through to the meat, and season to taste with salt and pepper.
Place the red peppers and the duck breasts in the centre of the grill (over the turned-off burner), sear skin down for 3 minutes and continue cooking for 9 to 10 minutes meat side down, finishing skin side down for another 3 minutes or until it reaches an internal temperature of 58°C (137°F). Cook carefully to prevent flare-ups. If you do get flames, flip the meat over and place it elsewhere on the grill. Turn the red peppers a few times while grilling.
Remove the peppers and duck from the grill, loosely cover the duck with aluminum foil and let it rest
Remove the skin from the breasts, and cut the meat in thin slices. Remove the skin from the peppers as well if you prefer.
Spread the inside of the buns with the spicy mayonnaise and pile with grilled peppers and cucumber. Add duck breast slices and top with spicy mayonnaise. Serve immediately with your choice of chips.
Recipe by Nicolas Vallée, Professional chef
Spicy fennel mayonnaise
In a sealed container, mix all the ingredients seasoning to taste with salt and pepper. Whisk well to combine and store in the refrigerator for at least an hour, allowing flavours to develop.