Preheat oven to 375° F.
Season both sides of brisket with sugar, salt, and pepper. Heat evoo in a large Dutch oven over medium-high heat. Add brisket and brown 5 minutes on each side. Remove from the pan and set aside.
Add apples to the pan, and cook 5 minutes or until nicely browned. Stir in thyme, and return brisket to the pan.
Add apple juice, cover, and bake at 375° F for 1 ½ to 2 hours, or until tender.
Remove brisket and apples from the Dutch oven and let rest.
Transfer the pan to the stove and bring liquid to a boil over medium. Simmer for 15 minutes or until reduced by half. Pour into a gravy boat or serving bowl.
Slice brisket into ¼-inch thick slices and place on a serving platter. Place cooked apples around brisket and serve with sauce on the side.