In a large stock pot, add the bacon pieces and cook for about 5 minutes.
Add the onion, celery, and butter. Cook for another 5 minutes, stirring frequently.
Sprinkle the flour over the mixture and continue stirring over medium heat for another 3 or 4 minutes.
Slowly whisk in the chicken broth and bring the soup to a boil. Lower the heat and allow it to simmer for about 15 minutes.
Add the milk and continue to simmer, without letting it come to a boil for another 10-15 minutes.
Remove the soup from heat and add the Tobasco, Worcestershire, and Sharp White Cheddar. Stir until the cheese is melted. (If you want a smoother soup, use an immersion blender at this point)
Mix in your desired amount of salt and pepper and serve the soup hot, garnished with chopped green onions.