Remove the skin of the duck breasts by pulling it off and slicing between the skin and the meat with a sharp knife. Cover and refrigerate the breasts.

Cut the duck skin into ¾-inch pieces.

Put the pieces of skin in a saucepan with the salt and 3 cups water, bring to a boil, and cook, uncovered, for 40 to 45 minutes, or until all the water is evaporated and the pieces of skin are sizzling in the rendered fat. Then continue frying the skin in the fat until it is brown and crispy, about 10 minutes.

Drain in a colander, reserving the fat for another use.

You need about 1 cup cracklings to serve with the duck; enjoy the rest with aperitifs.

Preheat the oven to 160 degrees.

Mix together the garlic, salt, pepper, vinegar, and both oils in a large bowl and set aside.

Heat the butter in a skillet until it is foaming. Sprinkle the duck breasts with the salt and pepper, add to the pan, and sauté over medium-high heat for 2.5 to 3 minutes per side for rare meat. Transfer the duck to a plate and set in the oven to rest for 5 to 10 minutes.

Meanwhile, deglaze the pan with the wine and water, mixing for a few minutes to melt and incorporate the solidified juices. Remove from the heat.

Reheat the cracklings in the microwave oven for about 45 seconds.

Toss the arugula with the dressing in the bowl and divide the salad among four plates. Place a duck breast on top of the salad on each plate and pour the deglazed juices on top. Sprinkle with the toasted nuts and cracklings and serve.