Prepare the potatoes, leek, onion, and celery.
In a large soup pot on medium high heat, melt 5 tablespoons butter. Add onion, celery and leek. Saute for 5 minutes.
Add flour and stir until well combined, about 5 minutes.
Add chicken broth, potatoes, salt, pepper, and thyme.
Stirring constantly, add milk and 1/2 and 1/2.
Bring to a low boil and lower heat.
Simmer for 15 minutes.
Stir occasionally so the soup doesn't stick to the bottom of your pot.
If the soup is too thick, adjust by adding more chicken broth or milk.
Turn off heat.
Cover and let sit for 15 minutes.
Serve with bacon bits, cheddar cheese, or fresh chopped chives.