Toss parsnips with 2 tablespoons olive oil in a bowl; spread parsnips onto a baking tray. Bake in the preheated oven until slightly tender, 20 to 25 minutes. Reduce oven heat to 180 C / Gas 4.
Toss apples and pears with 2 tablespoons olive oil in a bowl. Push parsnips to one side of the baking tray and spread apples and pears on the other side. Bake in the oven until fruit is soft and caramelised, 15 to 20 minutes.
Heat remaining olive oil in a large pot over medium heat. Cook and stir leeks in hot oil until leeks are soft, about 5 minutes. Sprinkle balsamic vinegar over leeks. Stir parsnips, apples, pears, chicken stock and rosemary into leeks. Bring to a simmer and cook until fruits and vegetables are completely tender and easily mashed against the side of the pot, about 20 minutes.
Puree the soup using an immersion blender or food processor until the soup is the consistency you like.