In a 6- to 8-quart stockpot over medium heat, fry bacon until crisp--about 15 minutes.
Remove bacon and drain on paper towels, reserving half pound for garnish.
In bacon fat, cook onions, carrots, and celery until the onions are translucent, about 5-7 minutes.
Add potatoes and cook for 5-10 minutes, stirring occasionally.
Whisk in gluten free flour and stir constantly over low heat until the flour is cooked and the mixture has thickened slightly, about 5 to 7 minutes.
Add chicken or vegetable stock and one pound of the bacon.
Season with salt and pepper.
Over medium-high heat, bring the soup to a simmer and cook for 25 minutes or until the potatoes are soft.
Add more chicken broth if necessary. (I used four cups).
Mash some of the potatoes for thicker, creamier texture, if desired. (I omitted this step).
Add whipping cream and simmer for 5-10 minutes or until soup thickens.
Season to taste, and garnish with toppings.