If the duck breast has been vacuum-wrapped, make sure to take it out of its package 1 h before cooking in order to dry it.
Keep the serving plates warm on the stove while you're preparing the dish.
Preheat the oven to 175°C/350°F.
Heat a thick-bottom skillet a couple minutes before cooking the breasts. Place the skin side down and lower the heat immediately to medium-low. Cook approximately 10 min until the fat has taken on a crisp quality. Remove the duck breasts from the pan and turn them over on a baking sheet (skin side up). Bake about 10 min for medium-rare. Pour off the liquid fat from skillet and put it aside in a small container in the refrigerator (Duck fat may be used to replace butter or oil in another recipe). Transfer duck to a cutting board, cover with aluminum foil and let stand 5 min before slicing.
In the meantime, finely chop the shallot and garlic. Heat the butter and oil in a pan over medium heat, sauté the shallot 2-3 min, then add the garlic. Cook 2 min, then delicately add the frozen raspberries to maintain their shape. Cook 2-3 min. Add the honey and vinegar. Reduce a few minutes, then add the demi-glace and apple juice.
After cooking for 2-3 more minutes, taste and adjust the seasoning: you may need to add salt, pepper and adjust the sweet-sour balance by adding more honey or vinegar. Keep warm.
Slice the duck, place on the warmed plates, coat with the sauce, sprinkle with the fresh chopped tarragon and serve.
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