Heat oil in a large pot over medium heat. Add the onions, carrots and celery. Sauté for 5 to 6 minutes or until tender. Add the potatoes and Tony Chachere's seasoning and stir to coat and combine.

Add around 6 cups of the vegetable broth or enough to cover the potatoes. Bring to a boil and then reduce heat to medium low and simmer for 20 minutes, or until potatoes are fork-tender.

Put the milk and flour in a bowl and whisk until completely combined and frothy. Slowly pour the milk and flour mixture into the soup and stir. The soup will slightly thicken as it continues to simmer.

Gently mash the potatoes with a potato masher, the back of a large spoon or you can use an immersion blender to smooth leaving it slightly chunky.

Add the heavy cream and additional broth if needed. Season with salt, black pepper and white pepper.

Serve the soup with your favorite toppings such as grated cheese sliced green onions.