Spray your pan with Pam® or similar.Add the onion, carrots, and celery to the pan and cook for 3 to 4 minutes until the onion is soft but not brown. Add the bacon crumbles to the pan with the water.
Add the peas to the pan with the thyme, bay leaves, potato, and ham or pork bone if you have one and bring to a boil. Lower the heat, cover, and simmer for 1 hour. (Check to see if more water needs to be added.)
Remove the thyme, bay leaves and bone. Process the soup with an immersion blender or food processor until desired texture. Return the mixture to the pot, add half and half, if using, and the diced ham/smoked pork. Reheat gently. Season with salt and black pepper. Ladle into soup bowls and serve.