Heat oven to 450°F. On a work surface, generously season lamb with salt and pepper. Transfer to a sheet tray and roast 30 minutes.
In a deep hotel pan, add onion, garlic, rosemary, tomato, vinegar, stock, and roasted lamb. Reduce oven temperature to 350°F. Cover pan and braise 2½ hours.
Let cool, then remove lamb and transfer to an airtight container. Strain braising liquid and pour over top of the roasted lamb. Cover and refrigerate overnight.
The next day, remove lamb from liquid and pick meat into bite-sized pieces, discarding bones and fat. Reserve braising liquid and lamb meat separately.
In a saucepan over medium heat, reduce reserved Lamb Leg braising liquid by three-quarters, or until a thickened sauce-like consistency is achieved. Stir in butter and mint. Reduce heat and keep warm.
Heat and prepare a wood-fired grill. On a work surface, generously season lamb with salt, pepper, and Ararat spice. Grill on all sides until internal temperature of the lamb reaches 125°F. Let rest 5 minutes, then cut into 2-bone pieces.
Heat oven to 450°F. Transfer lamb to a sheet tray and roast 30 minutes. Keep warm.
Bring a pot of salted water to a boil. Add beans and cook until soft. Strain and transfer beans to a Vitamix Commercial blender. Add butter, then purée until smooth, adding cooking water if necessary to thin. Taste and adjust seasoning with salt. Transfer mixture to a saucepan over low heat and keep warm.
In a sauté pan over medium flame, heat oil. Add fava beans and leaves and sauté until softened. Add Lamb Leg and cook until warmed through. Add butter, then season with salt and pepper.
In the center of a serving plate, place 1½ ounces Fava Bean Purée. Top with Lamb Leg-fava bean mixture followed by 1 portion Lamb Rack. Spoon Lamb Jus around the plate. Garnish with tomatoes and parsley.
