Combine the hot coffee, crushed cardamom pods and the whole cinnamon stick in a bowl. Let cool.
Prick the skin of the duck breasts all over with a sharp kitchen fork. 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 marinade over them, cover and refrigerate for at least 6 hours, or overnight.
Remove the duck breasts from the marinade and pat them dry with paper towels; discard the marinade. Heat a large skillet over medium-low heat. Add the duck breasts, skin side down, the whole cardamom pods and the broken cinnamon sticks and cook for three minutes. Scatter the coffee beans around the duck breasts and cook, gradually increasing the heat as the duck breasts render their fat, for about 4 minutes longer, or until the skin is crisp and brown.
Transfer the duck breasts to plate and discard the coffee beans and spices. Return the duck, skin side up to the skillet, add the port or Madeira and bring to a simmer over medium-low heat. Braise the duck breasts for 5 minutes. Remove from the heat and let stand 5 minutes to finish cooking.
To serve, cut the duck breasts into 1/2-inch thick slices and fan them out on four plates. Drizzle the pan juices over the duck and serve immediately with the Pear and Fingerling Potato Ragout.