Score the skin of the duck breasts in a crosshatch pattern with a sharp knife, being careful not to cut too deeply into the flesh. Season both sides generously with salt and pepper.
Place the duck breasts skin-side down in a cold skillet. Cook over medium heat until the fat is rendered and the skin is golden brown and crispy, about 8-10 minutes.
Flip the duck breasts and cook for another 4-5 minutes for medium-rare, or longer depending on your desired level of doneness.
Remove the duck breasts from the skillet and let them rest, loosely tented with aluminum foil, for 5-10 minutes.
While the duck is resting, trim the green beans and blanch them in boiling salted water for 3-4 minutes, then drain and immediately plunge them into ice water to preserve their vibrant color.
Melt the butter in a skillet over medium heat. Add the minced garlic and sauté for 1-2 minutes, until fragrant. Add the green beans, season with salt and pepper, and sauté for another 3-4 minutes.
Slice the rested duck breasts and serve with the garlic butter green beans. Garnish with fresh parsley.
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