Stir together mayonnaise, olive oil, garlic, turmeric, lemon juice and cayenne pepper in small bowl. Refrigerate at least 2 hours or up to 2 days. Stir well before serving.
Heat oven to 450 degrees F.
Combine 1 tablespoon olive oil, rosemary, 1/2 teaspoon salt and 1/2 teaspoon pepper in small bowl. Rub all over pork loin. Place pork, fat side up, in large roasting pan.
Roast pork in 450 degree F oven for 15 minutes.
Meanwhile, toss together sweet potatoes, parsnips, carrots, potatoes, onion and remaining oil, salt and pepper in second large roasting pan.
After pork has roasted for 15 minutes, lower oven temperature to 375 degrees F. Place vegetables in oven. Roast pork and vegetables in 375 degree F oven, stirring vegetables every 20 minutes, for 60 to 70 minutes or until instant-read meat thermometer inserted in pork registers 160 degrees F. Remove pork to serving platter and let stand 15 minutes. Pour off pan juices into bowl; skim fat from surface. If vegetables are not fork-tender, continue to roast. Once vegetables are tender, toss with reserved pan juice. Remove to serving platter. Slice pork; arrange on platter. Serve with aioli sauce.
