Preheat the barbecue to high heat, keeping one element off. Remove some of the excess skin from the ends of each breast, then make incisions in a checkerboard pattern in the skin without piercing the flesh. Add salt and pepper to taste. Set aside.
Cut the peppers in half and dress them. Place them on a large plate with the zucchini halves and drizzle with olive oil. Add salt and pepper to taste.
Place the vegetables on the barbecue grill and brown them. Do the same with the duck breasts over direct heat and sear for 1½ to 2 minutes, skin side down, turning them once. Continue cooking the breasts over indirect heat for 8 to 10 minutes, skin side down on the grill, and finish cooking over direct heat for 2 minutes, flesh side down on the grill. Keep an eye out for flare ups. If this happens, move the meat around and turn it over.
Remove the grilled vegetables from the barbecue along with the duck breasts, cover loosely with a sheet of aluminum foil and let stand for 5 minutes.
Cut the vegetables into large bite-size pieces and divide them between 4 plates. Slice the duck breasts into large pieces and arrange them on the plates. Top with the mint salsa verde and serve immediately with olive fougasse or an olive baguette. Garnish with mint leaves.
Place all the ingredients in a small, narrow container and using a hand mixer, reduce to a semi-smooth purée. Store in the refrigerator in an airtight container.