Using a sharp knife, score the duck skin (fat) with diagonal parallel slashes 1/2 inch apart to make a diamond pattern, being careful not to pierce through to the flesh.
Pour the balsamic vinegar into a shallow dish just wide enough to fit the breasts in one layer.
Add the duck, flesh (not fat) side down; cover and leave to marinate for 20 minutes at room temperature (can be marinated up to 2 hours refrigerated but remove for last twenty minutes at room temperature).
Heat a non-stick skillet over medium-high heat.
Add duck, fat side down and cook until crispy, about 5 minutes (covered to avoid spattering).
After the 5 minutes, carefully pour the rendered fat from the pan and wipe the outside of the pan of any grease that may have dripped there before placing back on the stove.
Turn the duck breasts over and continue to cook: about 5 minutes more for rare, 8 for medium rare, and 10 minutes for well done, but of course depending on the size of the duck breasts.
Remove duck from pan to cutting board and slice thinly against the grain.
Serve immediately, passing extra balsamic vinegar for drizzling if desired.