Preheat the oven to 375 degrees Fahrenheit.
Toss the onions, carrots, celery, turnips and Brussels sprouts, add a generous amount of the olive oil and season it with salt and pepper.
Pour the mixture into a roasting pan and place into a hot oven for 45 minutes or until caramelized, stirring and shaking the pan occasionally to prevent scorching and to make sure the vegetables cook evenly.
While the vegetables roast add the vegetable broth and chopped tomatoes to a large soup pot and bring to a boil.
Gently simmer for 15 minutes and then keep warm.
Add the parsley leaves, garlic, extra virgin olive oil and Parmesan cheese to a blender and puree till smooth.
When the vegetables have roasted, remove and transfer to the hot vegetable broth.
Bring to a boil over high heat.
Lower the heat and let the soup simmer until all of the vegetables are tender, approximately 30 minutes.
Divide the soup among four to six bowls and serve with a drizzle of parsley pesto.