Step 1Combine the coffee, crushed cardamom pods and whole cinnamon sticks in a bowl and allow the mixture to cool.
Step 2With a fork, prick the skin of the duck breasts all over. Then with a small, sharp knife, score the skin of each breast a few times. Place the breasts skin side up in a baking dish. Pour the coffee mixture over them, cover and marinate in the refrigerator for at least 6 hours or overnight.
Step 3Remove the duck from the marinade and pat dry with paper towels. Discard the marinade. Place the duck breasts, skin side down, in a large skillet. Add the cardamom pods and the broken cinnamon sticks and cook over medium-low heat for 3 minutes. (If you have six duck breasts, you may want to do this in two batches, dividing the cardamom pods and cinnamon sticks, but combine both batches of duck before adding the Port.)
Step 4Scatter the coffee beans (if working in batches, use half the coffee beans) around the duck breasts and cook, gradually increasing the heat as the duck breasts render their fat, about 9 minutes longer for 14- to 16-ounce breasts (5 minutes for smaller, 6-ounce breasts), or until the skin is crisp and brown. Transfer the duck breasts to a plate and discard the coffee beans and spices. (If working in batches, clean the pan and repeat with the remaining cardamom pods, cinnamon sticks, coffee beans and duck.)
Step 5Return the duck, skin side up, to the skillet, add the Port and bring to a simmer over medium heat. Cook the duck breasts for 7 to 9 minutes (about 5 minutes for smaller breasts). Remove them from the heat and let stand for 5 minutes to finish cooking.
Step 6Refrigerate the duck; remove from the refrigerator about an hour before serving to bring to room temperature.
Step 1Bring about 3 quarts of unsalted water to a boil in a saucepan. Add the lentils, remove from heat and let soak for an hour (they can soak overnight).
Step 2Drain and rinse the lentils. Bring another 3 quarts of water and 2 teaspoons salt to a boil. Add the lentils and boil until cooked but still firm. This can take only 2 minutes or longer, depending on the lentils; watch carefully so that they don't overcook and become mushy. Drain and rinse under cold water.
Step 3Make a vinaigrette from the olive oil and sherry vinegar, adding salt and ground pepper to taste.
Step 4Cut the greens into very thin strips (a chiffonade) and put them together in a large bowl. Add about half the vinaigrette and the green lentils. This can be done ahead of time; the flavors are better if they have time to stand and the greens have time to wilt.
Step 5Slice the duck breasts very thinly on a bias. Arrange on a plate and spoon the lentil salad beside the fanned-out duck. Spoon a tablespoon of the reserved dressing around the duck and sprinkle with fleur de sel and freshly ground black pepper. Serve immediately.