In a heavy bottomed pot, cook bacon over medium heat, until crispy. Set aside on a plate lined with a paper towel to absorb grease. Do not drain the bacon grease from the pot.
Add onion, celery, and carrot to the bacon grease. Saute until vegetables are tender. Add peas, water, potatoes, ham, salt, bay leaf, and pepper. Add ham bone, bring to a boil. Reduce heat, and simmer 45 minutes. Stir occasionally.
Remove ham bone and bay leaf.
Using a stick blender, blend ingredients until smooth. See recipe notes if you don't have a stick blender.
Add heavy whipping cream and stir until thoroughly incorporated. Crumble cooled bacon and use to garnish soup.
If you don't have a stick blender, allow the soup to cool and process the soup in small batches in the blender until smooth. Return processed soup to the pot and heat.