Score the duck breasts neatly down to the meat, but not through the meat. You want maximum fat scoring without any chance for the meat to drain its juices out.
Salt the duck heavily on the skin/fat side and lightly on the meat side.
If you have one, insert an RFX MEAT probe into the breast to track the temperature throughout the cook. Place the breasts skin-side down in a heavy pan, such as a cast-iron or heavy stainless steel pan. Turn on the heat to low-medium-low. Place another heavy pan on top of the breasts to keep them from curling up out of shape.
Cook the breasts slowly, maintaining a gentle bubble in the rendered fat—it should be moving and bubbling but should not be popping or splattering.
Every five or so minutes rotate the breasts in the pan for even browning. If the fat gets deep enough to start encroaching on the bare meat at the edges, pour some of it off into a container and save it for later.
As the fat more fully renders, start to check the temperature of the breast in the center with your Thermapen. (Move the weighting-pan first, obviously.)
When the internal temperature reaches 125°F (52°C) as verifies with your Thermapen ONE, increase the heat under the pan to medium for about a minute to finish browning the skin. Flip the breast over and cook for another 1–2 minutes until the internal temperature reaches 130°F (54°C). Remove the breasts from the pan and let rest, skin-side up, on a plate.