In a soup pot, cook diced bacon until crispy; remove bacon, leaving bacon grease.
Add celery and onions and cook over medium heat until soft.
Add garlic and cook 1-2 minutes.
Add potatoes and cook 3-4 minutes, stirring occasionally.
Add bacon and chicken stock to cover potatoes. Simmer, covered, until potatoes are cooked and soft.
Meanwhile, in a medium saucepan, melt butter over medium heat. Add flour and cook 1-2 minutes. Add milk and tarragon. Bring to a boil and, stirring contantly, cook until thickened. Remove from heat.
Add thickened sauce to cooked potato mixture. Blend half of this mixture in a food processor, if desired. Season with salt and pepper and serve.