1. Dry the duck skin well with paper towels. Use a sharp knife to cut a criss-cross pattern into the skin of each breast. The lines should be about ¼ inch apart across the whole skin and should cut into the fat below the skin without cutting through to the meat. Sprinkle the skin with kosher salt and gently rub into the cuts.
2. Place the duck skin-side-down in a cold PADERNO Canadian Classic Stainless Steel Cookware Set, Dishwasher & Oven Safe, 11-pc, 2L sauté pan. Turn the heat on medium low and cook for about 20 minutes without flipping or moving it until the skin is dark gold. As the fat accumulates in the pan, spoon it out into a bowl. Once the skin is deeply golden, flip the duck and cook for another 5 minutes for medium-rare (add 5 more minutes for medium). Transfer to a cutting board to rest for 5 to 15 minutes.
3. Drain the fat from the frying pan into the bowl, then add 2 tablespoons back into the pan. Add the shallots and cook over medium for 3 minutes or until softened. Add the flour and stir well to combine. Add the broth and vermouth and cook, stirring and scraping up any bits from the bottom of the pan, until the gravy is simmering. Stir in soy sauce. Taste and add more salt if needed.
4. Carve the duck into ¼ -inch slices. Spoon the gravy overtop.