Score the duck breast skin in a crosshatch pattern, being careful not to cut into the flesh. Season both sides with salt and pepper.
In a hot skillet over medium-high heat, place the duck breasts skin-side down. Sear for 6-8 minutes, until the skin is golden brown and crispy. Flip and cook for another 4-5 minutes.
Transfer the seared duck breasts to a preheated baking sheet and let them rest in a 350°F (180°C) oven for 8-10 minutes to ensure they remain juicy.
While the duck breasts are resting, prepare the orange sauce. In a small saucepan, melt the butter over medium heat, then add the brown sugar and lightly caramelize.
Pour in the orange juice and add the grated orange zest. Stir to combine. Add a pinch of salt and the rosemary sprigs.
In a separate small bowl, whisk together the cornstarch and water until smooth. Gradually add the cornstarch slurry to the sauce while stirring constantly. Cook until the sauce thickens.
Slice the rested duck breasts and serve with the orange sauce. Garnish with fresh rosemary.
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