Preheat the oven to 400 degrees F.
In a food processor, add the breadcrumbs, walnuts, garlic, shallot, arugula, and mushrooms. Process briefly until evenly combined. Add the olive oil, salt and pepper and pulse a few times. The mixture should be slightly moist and hold together in a ball when you squeeze it. If the mixture does not hold together, add another tablespoon of oil and pulse again. Transfer to a bowl.
Place the leg of lamb, opened and boned side facing up, on a large work surface, and spread the stuffing evenly over the surface of the meat. Roll the lamb up tightly and tie with kitchen twine every inch to hold together securely. Place in a roasting pan.
In a small bowl, combine the finely chopped rosemary and olive oil. Spread over the surface of the tied leg of lamb and sprinkle generously with salt and pepper. Pour over a 1/2 cup of the wine and transfer to the oven.
Roast, pouring a 1/2 cup of wine over the meat every 20 minutes, until browned and an instant thermometer registers between 140 and 145 degrees F when inserted into the thickest part of the lamb, about 1 hour and 20 minutes.
Remove the lamb from the oven, cover with foil, and let rest for 15 minutes before carving.
To serve, remove the string and slice into 1-inch thick pieces. Top with a drizzle of the jus from the roasting pan.
I like to serve this with mashed potatoes and a colorful vegetable like broccoli or carrots.