For the American Lamb: Liberally season the shanks with salt and pepper; set aside. In a large bowl, add onions, fennel, garlic and rosemary; toss to combine. Lay shanks on top of marinade, nestling each one into the vegetables until partially submerged. Pack marinade over and around shanks; refrigerate, uncovered, for 24 hours. 

Remove shanks from marinade; set aside. In a large Dutch oven or heavy-bottomed ovenproof pan with a lid, melt butter over medium heat. When butter is foamy, add lamb shanks; brown well on all sides, about 12 minutes total, in batches if necessary. Remove shanks to a plate.

Increase heat to medium-high; add marinade vegetables, cooking and stirring occasionally until slightly softened. Add wine; increase heat. Cook, scraping the bottom of the pan with a wooden spoon to loosen any browned bits, until the wine has reduced by half. Add the stock and bring to a simmer; add lamb shanks back to the pan. The liquid should come about halfway up the sides of the shanks. Put lid on the pan and place in oven. Cook at 350°F until lamb is fork tender and falling off the bones, 2 to 2-1/2 hours. 

For the Butternut Squash and Parsnip Puree: Peel the squash, cut in half and remove seeds. Cut halves into 1-inch chunks; set aside. Peel and slice parsnips into 1-inch coins; add to squash. In a large saucepan with a lid, warm the butter and oil over medium heat. When butter begins to get foamy, add garlic and leek. Cook, stirring occasionally, until leek softens slightly and become translucent, about 7 minutes. Add wine, water, squash, parsnips, paprika, herbes de Provence and salt; stir to combine. Bring to a boil over medium heat; reduce heat to a simmer and cover. Simmer until vegetables are very soft, about 30 minutes. Remove pan from heat; allow contents to cool slightly. In a food processor, puree vegetables in batches to achieve a smooth and silky consistency. Season to taste with salt and serve warm with the braised lamb shanks.

For the American Lamb: In a mini food processor (or with a knife), finely chop garlic, rosemary, and oil until garlic is a paste and rosemary is a mix of some finely chopped and some larger leaves. Season lamb rack on both sides with salt and pepper; then rub with the garlic-rosemary mixture. Set aside at room temperature for about 1 hour. 

For the Maple-Roasted Brussels Sprouts, Delicata Squash and Pears: Halve the squash lengthwise; scoop out seeds. Cut into 1/2-inch-thick moon-shaped slices. Pile the squash, sprouts and pears in the center of a large rimmed baking sheet. Drizzle with oil and maple syrup; sprinkle with a few big pinches of salt and several grinds of pepper. Toss to coat evenly; spread the mixture in a single layer on the baking sheet. Place the lamb meaty side up in the center of the pan, covering some of the vegetables and pears. 

Roast at 475°F until internal temperature reaches 130°F to 135˚F on an instant-read thermometer for medium-rare, 10 to 15 minutes. (The internal temperature will increase to 145˚F out of the oven.) Transfer rack to a large platter; cover loosely with foil to rest for 10 to 15 minutes. Transfer lamb back to the baking sheet; roast again in the upper third of the oven until vegetables are tender and the internal temperature of the lamb reaches about 120°F on an instant-read thermometer, 25 to 30 minutes. 

Switch the oven to broil; position the sheet pan so the top of the lamb is about 4 inches from the broiler. Broil until lamb and vegetables are nicely browned on top, 3 to 5 minutes. 

Transfer the rack to a carving board; tent it with foil, let it rest for 10 minutes. Loosen pears and vegetables from the baking pan with a spatula, scraping up any browned bits from the pan; toss them together with the parsley. Transfer to a warmed serving platter.

 Carve the rack between the rib bones; transfer to the platter, nestling it over the vegetables and pears. Serve immediately, with Syrah wine.

Season American lamb shanks all over with salt and pepper. 

Heat a large Dutch oven over medium heat; add oil and heat through. Add lamb shanks; brown on all sides, about 4 minutes per side. Remove to a plate and set aside. 

Return the Dutch oven to heat; add carrots, celery, onion, and squash; sauté until onions are soft, about 5 minutes. 

Add wine; bring to a boil. Add stock, thyme, cinnamon stick, and bay leaf. Return lamb shanks to the pot; bring mixture to a simmer. Cover tightly; transfer to the oven. Braise shanks at 325°F, turning once, until fork tender, about 2 hours. Discard thyme, cinnamon and bay leaf. 

Divide lamb shanks between serving bowls; ladle vegetables and braising liquid over the top. Serve hot with mashed potatoes.

Heat a cast iron or non-stick heavy-bottom skillet over medium to medium-high heat. Melt butter in the pan; sear chops in 2 batches for 2 minutes per side. Add rosemary, garlic, thyme, salt and pepper; reduce heat to medium. Baste chops with herbs and garlic butter; use a spoon to pour the juices over the chops while the pan is tilted away from you. Do not burn the butter or drippings. Remove chops to rest; add onions and apples to the pan. Sauté for 6 to 8 minutes until apples are tender and translucent and onions begin to caramelize. 

Serve lamb chops with apples and onions alongside a green salad or couscous.