To butterfly, unroll the lamb and, using a sharp knife, make deep cuts into the thick parts to open the meat out like a book. Trim any excess fat and remove any silver skin. Silver skin is connective tissue that looks shiny and won't tenderize with cooking. Once the lamb is prepped, place in a large ziploc bag or container.
In a small bowl, whisk together the olive oil, lemon juice, minced garlic, dried oregano, dried mint, kosher salt and pepper. Pour the marinade over the lamb and seal the bag. Refrigerate the lamb for at least 2 hours or preferably overnight. Flip the lamb several times while marinating.
Feta Yogurt Dressing
Roughly chop the parsley and fresh mint leaves. In a food processor, combine half of the yogurt, the crumbled feta cheese and the minced garlic. Add the zest of one lemon along with juice from one half of the lemon. Reserve the other half lemon for the salad. Add the chopped parsley and mint, kosher salt, and pepper. Blend until the herbs are finely chopped.
Transfer the mixture to a bowl and whisk in the remaining yogurt. Whisking in the remaining yogurt will help to thicken the dressing. Chill until ready to serve.
To Serve
Take the leg of lamb out of the fridge 30 to 60 minutes before you intend to grill it. Heat a grill, or barbecue, until the temperature reaches between 450°F and 500°F.
Lightly grease the grill grate and place the lamb directly on the grill. Grill on one side for 7 to 10 minutes. Rotate the lamb half way through the cooking time if you want to create grill marks. Flip the leg lamb over and cook on the other side until it reaches an internal temperature between 130°F and 135°F.
Remove the leg of lamb onto a serving platter and tent with foil. Allow to rest for 15 to 20 minutes.
While the lamb is resting, prep the arugula salad. Toss together the baby arugula and fresh mint leaves. Squeeze the remaining half lemon over the greens and drizzle with a little olive oil. Sprinkle the salad with kosher salt and toss together.
Thinly slice the leg of lamb, making sure to cut against the grain. Arrange the lamb slices on a large serving platter and drizzle with the feta yogurt dressing. Top with the arugula mint salad and enjoy!