Preheat a large skillet over medium-high heat (375°F/190°C).
Meanwhile, prepare the Duck Salami (Fresh) breast. Rinse it under cold water and pat completely dry with paper towels. Use a sharp knife to remove any silver skin from the meat side. Trim off excess fat, leaving a layer about 1/4-inch thick.
Place the duck breast skin-side up on a cutting board. Use your knife to score the skin and fat in a crosshatch pattern, making diagonal cuts about 3/4-inch apart. Cut through most of the fat layer, but be careful not to cut into the meat.
Season both sides of the duck breast generously with the salt and pepper.
When the pan is ready, place the duck breast skin-side down. You should hear it sizzle immediately. You don't need to add oil - the duck will release its own fat.
Cook for 8-10 minutes, occasionally draining off the rendered fat into a bowl (strain and save it for another use). The skin should become deep brown and crispy. Check the edges of the duck breast - the meat should be cooked about 1/3 of the way up from the bottom.
Flip the breast over, reduce heat to low, and cook for another 4-5 minutes for medium-rare, or until the internal temperature reaches 135-140°F.
Transfer the duck to a cutting board and let it rest under a tent of foil for 5 minutes before carving.
Meanwhile, drain off all but 1 tablespoon of fat from the pan. Return the pan to medium heat (350°F/175°C).
Add the honey to the pan and stir to dissolve.
Add the vinegar and stir to combine. Continue to cook, stirring constantly, for another 30 seconds. Turn off the heat and swirl in the olive oil. Season to taste with salt and pepper.
Cut the duck breasts diagonally into 1/4-inch thick slices. Fan them out on two warm serving plates.
Drizzle the honey sauce over each portion and serve immediately with lightly dressed salad greens on the side.
