Pour uncooked navy beans into a large pot full of cold water. Let soak overnight on kitchen counter.
Remove all floating beans and shells, drain and set aside.
Using the same large pot, add ham bone, ham pieces, bay leaves, carrots, celery and water.
Make sure to keep at least three inches of liquid above the beans at all times.
Cover and cook on low-medium heat for 3 hours. Stir occasionally.
Add in potatoes and cook for 2 additional hours.
Remove the ham bone from the pot and make sure all ham pieces are bite-sized.
Check potatoes (tender to the fork) for doneness.
To make the dumplings, mix the eggs, flour, salt, and water in a medium sized bowl.
If the mixture is too dry, add in a tiny amount of water. Dumpling consistency should be slightly sticky.
Use a spoon to scoop dumpling mixture (nickel size), carefully drop into hot soup.
Add water in small increments to the soup as the dumpling are cooking, they will soak up the juices.
Stir and cook for another 20-30 minutes until dumplings are cooked.