Cover navy beans with water and soak overnight (approximately 8 hours).

Drain the soaked beans.

Place the drained beans in a large pot and cover with a large amount of fresh water.

Add the ham bone shank to the pot.

Bring to a simmer and cook until the beans are almost soft (about 2-2.5 hours).

Skim off any fat that rises to the surface during cooking.

Add the tomato paste, diced potatoes, chopped onions, and celery to the pot.

Season with salt and pepper to taste.

Continue to cook until the vegetables are soft (about 20-30 minutes).

Remove the ham bone shank from the soup.

Serve the soup as is, with whole beans, or mash the beans to a creamier consistency.