- Sort through the dried split peas and discard any grit or discolored peas. In a bowl, place peas and enough water to cover. After a minute, remove any peas or skin that float to top. Rinse split peas and drain well. 
- In a large pot over medium heat, heat olive oil. Add onions, garlic, carrots and celery. Cook, stirring regularly, until softened. 
- Add water and bring to a boil.  
- Add dried split peas, ham bone, and bay leaves. Bring to a boil, skimming off scum that may float on top.  
- Lower heat, cover and simmer for about 1 1/2 to 2 hours or until peas are tender.  
- In the last 30 minutes, add potatoes and cook until very tender. Using back of spoon, mash potatoes to help thicken soup. 
- Remove ham bone and scrape meat from bone. Chop ham meat and return to pot.  
- Season with salt and pepper to taste. Ladle into serving bowls and serve hot.