1. Flatten chicken breast until 1/4 inch thick. Place ham and cheese in the center of the flattened chicken breast and sprinkle with thyme, parsley, salt and pepper. Roll up chicken breast around filling and secure with tooth picks. Brush 1 1/3 tsp oil onto a baking dish. Place rolled chicken in dish and cover tightly. Bake in a preheated 350-degree oven for 30-40 minutes.
2. Heat remaining oil in a medium non-stick saute pan, then add leeks, celery, mushrooms, and green beans. Cook for 3-5 minutes. Spoon vegetables onto serving plate and top with rolled chicken breast.