In a stockpot, cook chopped bacon over medium heat until crisp. Remove from pan and set aside. Leave about 2 T. of bacon drippings in the pot.
Add celery, carrots, and onions and saute for about 5-7 minutes until crisp-tender.
Add chicken broth, potatoes, salt, pepper, and bay leaf.
Boil for about 10-15 minutes until potatoes are fork-tender.
Add cream and milk and stir to combine.
At this point you may mash part of the potatoes to thicken the soup a bit. I prefer to leave some chunkiness to the soup so I don't mash completely, but it's up to your preference.
Simmer for about 5 more minutes until soup is thickened and hot.
Top with reserved bacon and shredded cheddar cheese if desired.