Begin by putting two tablespoons of butter in the stock pot. Chop up the half an onion to whatever size you prefer for soup.
Cook the onions in the butter, stirring occasionally, until they are translucent.
Remove the onions and set aside.
Pour in the six cups of chicken broth.
Rinse the ham hocks under cool water, then add them to the broth.
Bring to a boil, then reduce heat to a simmer and cover.
Cook at a low simmer for about an hour, until the meat is starting to come off the bones a little.
While the hocks simmer, wash then chop up the carrot and potato.
After the hocks have been simmering for an hour, add the carrots and potato to the pot.
Cover again, and allow to simmer for another half hour or so. When the carrots and potatoes can be poked through with a fork, it is done.
Remove the hocks from the soup and pull off the meat. This can be done with a fork, knife, and most likely with your fingers as the meat can be pretty slippery.
Set the meat aside.
Add the onions back to the pot.
For a smooth soup, blend the entire pot of ingredients. Be sure to never fill a blender more than half full.
For a slightly chunky soup, blend half the vegetable ingredients, then add them back to the broth.
Return the ham to the pot and stir it in.
Serve as is or with a garnish of parsley, sour cream, and cheddar cheese.