Preheat the oven to 350°F. To help duck skin crisp up, dry it with a paper towel, then score the fat, being careful not to pierce the meat. Season all sides with salt and pepper. Heat oil in a large skillet over medium-high heat until shimmering hot. Add duck breasts, skin-side down, and cook over medium heat until the skin is golden brown, about 10 minutes. Turn the breasts over and sear the meaty side for 3 minutes. Carefully remove the fat from the pan and deposit it in a heatproof container. When cool, cover, refrigerate, and save the duck fat for another time (it is liquid gold)! Transfer the skillet to the preheated oven and roast breasts about 5 minutes for rare. An instant read thermometer inserted into the center of the breast will read 140°F; or 8 to 10 minutes for medium rare, about 150°F. Transfer the breasts to a plate and cover loosely with foil. While the duck rests, prepare the sauce. Combine jam, orange juice, vinegar, and sugar in a small saucepan. Cook over medium-high heat until the sauce begins to bubble. Reduce heat to a gentle simmer and cook 10 minutes, or until the sauce reduces by half and becomes syrupy. Slice the duck breasts on the diagonal. Place one-half breast on each of 4 plates, drizzle the sauce over the sliced duck.