Heat the oven to 300°.
Pat the lamb shoulder very dry. Season the meat on both sides with salt and black pepper and set aside at room temperature for 30 minutes.
Glaze the bottom of a heavy, 6-quart Dutch oven or roasting pan with olive oil about 1/8-inch deep and set over medium-high heat.
When the oil is shimmering hot, add the lamb shoulder and sear until deeply brown—about 10 minutes. Turn the meat and brown on the other side. Remove from the heat and place the meat on a platter.
Carefully pour off the fat from the pan, leaving the caramelized meat glaze on the bottom. Arrange all of the vegetables, herbs and whole cloves in the pan.
Place the lamb on top of the vegetables and pour any accumulated juices from the platter over the meat. Add the lamb stock to cover.
Roast, uncovered, in the preheated oven for 2½ hours, then turn the meat and roast an additional 2½ hours.
While the lamb is cooking, make the rosemary demi-glace: Combine the beef and lamb stocks with the rosemary sprig in a heavy-bottomed, 4-quart saucepan over medium-low heat.
Cook the stocks slowly—stirring occasionally—until they become syrupy and have reduced to about a fifth of their original volume, or about ¾ cup.
Add the syrah and cook to reduce slightly until the syrupy consistency returns. Strain the demi-glace, discard the rosemary sprig and set aside.
Melt the butter in a heavy-bottomed skillet over medium-high heat. When the butter has melted and foam subsides, add the shallots and cook until wilted and transparent, about 6 minutes.
Whisk in the demi-glace vigorously and season to taste with salt and freshly ground black pepper. Set aside to keep warm.
Once the meat has cooked, remove it from the pan, let it rest for 15 minutes then cut it into serving pieces. Cover with foil to keep hot.
Strain the pan juices through a fine strainer or chinois into a bowl—pressing down on the aromatics to squeeze out all of the liquid. Discard the aromatics, wipe the roasting pan clean and set aside.
Pour 1 cup of the strained pan juices into a heavy-bottomed, 2-quart saucepan over medium-high heat. Add the Marsala and cook until reduced by a third.
Remove from the heat and vigorously whisk in the butter cubes all at once. Continue to whisk until the butter has melted and the sauce is smooth and thick.
Heat the broiler and place an oven rack 6 inches below the heat source. Arrange the serving pieces of meat in the cleaned roasting pan and pour the Marsala glaze over them. Place the pan under the broiler for 2 to 3 minutes. Take extreme care not to burn the meat.
To serve, either place a portion of the meat on each plate and spoon the demi-glace over each, or serve the meat on a platter and pass the sauce separately.