4 lamb shanks (10 to 12 ounces each)
1 bunch rosemary
1 head garlic, smashed; peel half of the cloves
1/2 cup malbec
1 tablespoon grated lemon zest
2 teaspoons smoked Maldon sea salt, plus more as needed
1 teaspoon freshly ground black pepper, plus more as needed
1 teaspoon piment d'espelette (ground espelette powder; may substitute sweet paprika; see headnote)
2 tablespoons red wine vinegar
About 1 cup extra-virgin olive oil, preferably South American
1/4 cup packed chopped flat-leaf parsley
3 small bunches medium-size stem-on carrots, scrubbed well
1 tablespoon chopped thyme
6 ounces good-quality goat cheese (in a log), cut into 1/2-inch-thick rounds
2 bunches arugula, rinsed and dried (about 1 3/4 pounds)
Combine the lamb shanks, all but 1 sprig of the rosemary, the unpeeled garlic cloves, all of the wine and the lemon zest in a large zip-top bag. Seal and massage to coat the shanks thoroughly. Marinate for at least 2 hours or in the refrigerator overnight.
Preheat the oven to 400 degrees. Have a roasting pan at hand that's large enough to hold the lamb shanks.
Remove the shanks from the bag, reserving the marinade. Season them all over with 2 teaspoons of smoked salt, the black pepper and the piment d'espelette, placing them in the roasting pan along with their marinade as you work. (Discard the skins of the roasted garlic and the spent rosemary.) Roast for about 45 minutes or until the shanks begin to show some caramelization; turn them over and cook for 45 minutes or until the meat has begun to pull away from the bone. (The total cooking time may be longer or shorter than the suggested 1 1/2 hours, depending on the size of the shanks.)
Allow the shanks to rest for 15 to 20 minutes, then add the vinegar, 8 tablespoons of the oil, the chopped parsley and the remaining peeled garlic cloves to the roasting pan. Place the pan (with the shanks in it) over medium-low heat and gently warm through for less than 1 minute; reserve the pan mixture as the sauce for the dish.
Cut the carrots in half lengthwise and place in a mixing bowl. (Depending on their size, cut the carrots into shapes that allow a surface area for charring.) Mince the remaining rosemary leaves (to yield 2 teaspoons) and add to the carrots, along with 3 tablespoons of the oil and the thyme. Season with salt and pepper to taste.
Heat a large cast-iron skillet over high heat. Add the carrots in a single layer, cut side down, leaving plenty of room around them. Allow them to char irregularly. Depending on their size, cook the carrots for 5 to 7 minutes with the understanding that they are meant to be overcooked toward the tips and slightly undercooked toward the top. Turn the carrots only once to ensure they char well. Transfer to a plate.
Keep the cast-iron skillet over high heat. Add 1 to 2 tablespoons of oil and swirl to coat the bottom, then add the goat cheese rounds; cook briefly, just until they develop crisp, dark edges, then transfer them to the lamb shanks, draping them over each one.
Add the arugula to the hot skillet; cook undisturbed just until the leaves blister. Season with smoked salt to taste, then drizzle with the remaining oil. Remove from the heat.
When ready to serve, divide the charred carrots among individual plates, using them to form a raftlike base. Place a lamb shank on each portion, then top with the blistered arugula and some of the warmed pan mixture.