Lay the duck breasts skin side up on a cutting board and pat them very dry with paper towels, then sprinkle both sides with kosher salt and black pepper.

Use a sharp paring knife on the cutting board to lightly score the skin in a crosshatch pattern, cutting through the fat but not into the meat.

Let the duck cook skin side down until the skin is deep golden and crisp and a good amount of fat has pooled in the skillet, then flip the breasts with tongs and cook the meat side just a few minutes until done to your liking.

Move the duck breasts to a clean cutting board with tongs and let them rest while you make the sauce, leaving a thin layer of duck fat in the skillet.

Add the raspberry jam, chicken broth, balsamic vinegar, lemon juice, and a pinch of kosher salt to the skillet or a small saucepan and stir with a wooden spoon over medium heat.

Let the sauce simmer a few minutes, stirring with the wooden spoon, until it looks glossy and slightly thick but still pourable, then turn off the heat.

Slice the rested duck breasts on the cutting board with a sharp knife, fan the slices on plates, and spoon the warm raspberry sauce over the top with the wooden spoon.