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, Tony Chachere's seasoning (or your favorite creole seasoning), and smoked paprika. Stir to coat and combine all of the seasonings.
Add 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 or the back of a large spoon leaving some chunky pieces for texture.
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 smoked Gouda sliced green onions.