Preheat oven to 400ºF. Pat duck dry and trim off any excess fat. Score skin in a crosshatch pattern at 1/2-inch intervals with a sharp knife; this will allow duck fat to escape as the breasts cook. Season with salt and black pepper on both sides, but don’t go overboard; broth will add some saltiness. Heat a 12-inch ovenproof, nonstick sauté pan or skillet over medium-low heat. Place duck breasts, skin side down, in the heated, dry skillet. No oil or other fat is needed—the duck will produce plenty. Cook the breast until the skin is crispy and most of the fat has rendered, about 10 to 12 minutes.

Transfer breasts to plate and pour the fat from the pan into a bowl, reserving it. Return duck breasts to the pan, skin side up, and place in the hot oven for 5 to 10 minutes, until an instant-read thermometer inserted diagonally into center registers 125°F for medium rare. Unlike chicken, this is perfectly safe—and delicious—so check at 5 minutes so you don't overcook. Remove from the oven. Transfer breasts to cutting board, tent with foil and allow to rest.

While duck rests, reheat pan over medium-low heat. Add 1 tablespoon reserved duck fat, then add pear wedges and sauté until golden brown, 2 to 3 minutes per side, turning gently and occasionally swirling pan to make sure pears are cooking in the fat, not scorching in a dry pan. Add shallots, garlic, tarragon and sugar and cook, stirring, until fragrant—a minute or so. Stir in vinegar, brandy and broth, scraping up brown bits. Let it cook down just slightly, about 5 minutes, then swirl in butter bits until they melt and combine.

Meanwhile, slice duck breasts into 1/4 to 1/2-inch slices. Fan on individual plates along with pear slices and top with sauce. Serve. I served these with white rice and spooned some of the sauce over it.