In medium bowl, combine oil, vinegar, chopped garlic, 1 sprig thyme, 1 sprig rosemary, salt, and pepper. Add duck, cover with plastic wrap, and marinate, turning occasionally, overnight in the refrigerator.
Remove duck from marinade, and pat dry with paper towels; discard marinade. Set aside. Place a heavy-bottomed skillet over medium heat. Add duck, skin-side down, and cook until the skin is browned and crispy, about 8 minutes. As excess fat accumulates, drain into a heatproof bowl and reserve. Increase heat to medium-high; turn duck, and cook for 5 minutes. Transfer to cutting board; allow to rest for 10 minutes before slicing.
Meanwhile, pour reserved fat into a cast-iron skillet over high heat. Add potatoes; when just beginning to brown, add picked rosemary, thyme, and remaining unpeeled garlic. Saute until potatoes are crispy and golden, 6 to 8 minutes.
Just before serving, slice duck across the grain into 1/2-inch-thick slices. Fan out decoratively between two plates. Garnish each with a rosemary sprig; serve with potatoes.