Combine the lamb with all the ingredients and turn to coat. Let stand for 20 minutes, then cook on a griddle over medium-high heat for 2-3 minutes per side, or to desired doneness.
Meanwhile, heat the oven to 500°F and place a rack in the center of oven. Toss the beans, tomatoes, shallots, garlic, oregano sprigs and olives in olive oil to lightly dress, salt and pepper. Turn out onto a sheet pan and roast until tender and the tomatoes burst, 25-30 minutes. Top with feta crumbles to serve.
While the beans and tomatoes roast, place the potatoes in small pot. Add the salt and pepper, milk, garlic and EVOO and bring to a simmer. Partially cover and cook to tender, 15 minutes. Drain and reserve the liquid, then push the potatoes through a ricer, adding as much liquid back as you like to yield very smooth and creamy garlic potatoes.
Serve the lamb chops with the potato Skordalia and roasted veggies alongside.