Marinate the lamb with the thyme leaves, half the rosemary and all the garlic. Cover and refrigerate at least 4 hours, preferably overnight.
Take the lamb out of the refrigerator 1 hour before cooking, to bring it to room temperature. After 30 minutes, sprinkle the lamb generously with salt and pepper.
Preheat the oven to 325 degrees F.
Heat a large saute pan over high heat for 3 minutes. Swirl in the olive oil, and wait a minute or two, until the pan is very hot, almost smoking. Place the lamb in the pan and sear it on all sides until well browned and caramelized.
Transfer the lamb to a roasting rack and reserve the pan. Arrange the thyme sprigs and remaining rosemary on the lamb and top with the butter.
Roast the lamb until an instant-read thermometer inserted into the center reads 120 degrees F. Let the lamb rest at least 10 minutes before slicing.
Arrange the greens on a plate and lay the sliced lamb over the top. Spoon some of the Lamb Sauce and Salsa Verde over the meat.
In a hot, heavy-bottomed pan, heat the olive oil and brown the meat bones well on all sides. Transfer to a deep pot.
Remove a bit of the oil from the pan, and then add the onions, carrots and celery and cook until caramelized. Deglaze with the red wine and reduce to a syrup. Transfer to the pot with the bones. Add the veal stock, thyme and bay leaf to the bones and bring to a boil. Skim and bring down to a simmer. Reduce the sauce by half, then strain. Cool and skim any excess fat that rises to the top.
In a mortar and pestle, gently pound the parsley, mint and marjoram to a paste. (You may have to do this in batches.) Work in some of the olive oil and transfer to a mixing bowl. Pound the anchovy and garlic to a paste and add to the herbs.
Gently pound the capers until they are partially crushed and add to the herbs. Stir in the remaining oil, a pinch of pepper and a squeeze of lemon juice. Taste for balance and seasoning.