The technique here is very simple. I use a similar one for my Chicken Fajita recipe (https://alpharaposashearth.wordpress.com/2018/02/28/simple-chicken-fajitas/). If you have cast iron, or a steel skillet with an oven-safe handle, it’s the best way to cook many different kinds of meats.
For duck breast, set the oven for 400 degrees F.
Rinse and pat the breasts dry. Carefully score the skin side- you want to cut through the skin and some of the fat, but not quite all the way to the meat. Simple slashes are enough. You can do a criss-cross (diamond) pattern if you want to do more.
Warm up some olive oil in a skillet over medium-high heat. Salt your duck breasts.
When the oil shimmers, lay the breasts, skin side down, into the skillet. Leave (don’t move) for 5-8 minutes, while the fat under the skin renders out.
This is a good place to use a spatter screen if you have one.
Once most of the fat is rendered out, flip the breasts over and cook on the other side just two minutes.
Remove most of the rendered fat, leaving a thin layer at the bottom, before placing the skillet in the hot oven. Cook until the internal temperature reaches at least 135 degrees (medium rare), another 15-20 minutes.
Remove from pan and let rest 7-10 minutes. Slice thinly. Serve with a sweet fruit sauce, such as cranberry sauce, or Cherry BBQ Sauce (https://alpharaposashearth.wordpress.com/2017/12/12/cherry-bbq-sauce/)