Quarter plums and remove pits. Melt the butter in a saucepan over medium heat.
Add the shallot and cook until soft, 3-4 minutes. Add plums and cook for another 3 minutes, then add honey and cook for 1 more minute, stirring often. Add cinnamon, 1/2 tsp salt, stock, and wine and bring to a simmer, then reduce to medium-low heat and cook for about 15 minutes, or until plums soften but don’t completely fall apart. Set aside.
With a sharp knife, score the skin of the duck into a cross-hatch pattern, being careful not to cut into the meat. Rub the skin with a pinch of kosher salt, and lightly salt the flesh sides.
Place the breasts skin-side down in a cast iron or stainless-steel skillet and turn heat to medium-high. Once the skin starts sizzling, reduce heat to medium and cook for 15 minutes for large breasts and 8 minutes for small, or until skin is nice and browned and lots of liquid fat has rendered out. Flip the breasts over and sprinkle the tops with black pepper.
Cook until interior temperature reaches 130°F for medium rare or 140° for medium (a few minutes). Remove from pan and let rest for 5-10 minutes before slicing. Reserve rendered duck fat for another use (try frying potatoes in it!).
To plate, divide the slices of duck breast evenly between 4 plates, perching them on top of colcannon (which I did), mashed potatoes, polenta, grits, or egg noodles. Briefly heat up the plums if necessary and pile next to the duck, drizzling some of the liquid over it while do. Enjoy!