How to Make It
In a small bowl, cover the raisins with the vinegar and 1/2 cup of the stock and let stand for 10 minutes.
Melt the butter in a medium sauce-pan. Add the shallot and cook over moderate heat until softened, about 4 minutes. Add the raisin mixture along with the honey and herbs and simmer until syrupy, about 5 minutes. Let cool, then transfer to a blender and coarsely puree.
Using a sharp paring knife, score the duck skin in a shallow crosshatch pattern, spacing the cuts about 3/4 inch apart. Heat the olive oil in 2 medium skillets until shimmering. Add the duck breasts, skin side down, and cook over moderate heat until the skin is deep golden, about 15 minutes; spoon off the rendered fat as it accumulates in the skillets. Season the duck breasts with salt and pepper, turn and cook until browned on the bottom and an instant-read thermometer inserted in the thickest part registers 135°, about 12 minutes longer. Transfer the duck breasts to a cutting board and let rest for 5 minutes.
Meanwhile, wipe out the skillets. Add the remaining 1/2 cup of chicken stock to 1 of the skillets and cook over moderate heat, scraping up any browned bits from the bottom of the pan. Scrape the pan sauce into the second skillet and cook over moderate heat, scraping up any browned bits from the bottom of the pan. Stir in the raisin puree and cook over moderate heat just until thickened, about 1 minute. Season the sauce with salt and pepper and transfer to a small bowl.
Thickly slice the duck breasts on the diagonal and arrange on plates. Spoon the raisin compote alongside and serve.