Step 1 Combine the coffee, crushed cardamom pods and whole cinnamon sticks in a bowl and allow the mixture to cool.
Step 2 With 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.