Position an oven rack in the lower third of the oven and heat the oven to 300°F.
Arrange four 16×16-inch squares of heavy-duty aluminum foil on a work surface. Put one-quarter of the leeks, one-quarter of the carrots, 1 rosemary sprig, and 1 strip of orange zest on each square. Season each with a pinch of crushed red pepper flakes, salt, and pepper. Set aside.
Pat the lamb shanks dry and season generously with salt and pepper. Heat the oil in a large skillet over medium heat until shimmering hot. Working in batches if necessary to avoid crowding, brown the shanks on all sides, about 10 minutes total per batch. Transfer 1 shank to each foil square, arranging it on top of the vegetables. Draw up the edges of the foil to capture any juice, but don’t seal the packets yet.
Return the skillet to medium heat, add the vermouth, and bring to a simmer, scraping the skillet with a wooden spoon. Remove from the heat. Portion the vermouth evenly among the 4 packets, pouring it over the lamb. Dot each shank with a slice of the butter.
Fold the foil to form rectangular packets, sealing the seams tightly. Arrange the packets on a baking sheet; it’s fine if they touch but they shouldn’t overlap. Bake for 2-1/2 hours; then check for doneness by carefully opening one of the packets (watch out for the steam) and testing the meat with a fork—it should be tender and pulling away from the bone. If necessary, continue to bake for another 10 minutes and check again.
Transfer the contents of the packets to large plates or pasta bowls, surrounding the shanks with the vegetables and juice. Remove the rosemary and orange zest before serving, if you like.
