Place the ham bone in a large stock pot or dutch oven and fill with warm water.
Add the split peas and vegetable soup mix, and bring to a boil.
Turn down the heat and let simmer for about two hours, turning the bone occasionally and adding more water as needed, until the meat is tender and falling off the bone.
Remove the ham bone from the pot and set aside to cool.
Add the carrots, potatoes, and extra ham (from the ham steak) to the pot and turn the heat up to medium to cook the vegetables.
When the ham bone is cool, pick off all of the meat and add it to the pot. Discard the bone.
Cook the soup until the carrots and potatoes are fork tender, adding more water if necessary as it simmers.