Preheat the oven to 425°F. Roast the lamb trimmings and garlic in a heavy-bottomed pot until golden, about 15 minutes. Remove the trimmings and set aside; stir in the shallots and roast until golden, 10 minutes.
Remove garlic from pot and set aside. Place pot over medium-high heat and pour in the wine. Cook while stirring often until reduced by two-thirds. Return trimmings to pot, add enough water to cover, and bring to a boil. Simmer gently for 45 minutes. Turn off the heat, strain, and set aside.
Peel the parsnips, slice off the tops and then blanch the parsnips in a large pot of salted boiling water for 2 minutes. Transfer to an ice water bath to stop the cooking, remove, and set aside.
Season the lamb chops with salt and pepper and place a few parsley leaves on top of each chop. Wrap with prosciutto leaving the bone exposed (the seam should be under the chop). Pan-sear the chops, parsley-side down, in a lightly oiled large skillet until browned. Turn over and add the butter, bay leaves, and roasted garlic (if using a smaller skillet, cook the lamb in batches). Cook until browned, turn the chops, and cook 8 minutes more. Set the chops aside and place the blanched parsnips in the pan. Brown on all sides, pour in the strained lamb jus and simmer for 1 minute. Serve the chops with sauce, parsnips, and chopped parsley.