Split Pea and Ham Soup!

So, as with Thanksgiving, you want to find a use for the leftovers besides making sandwiches.  This soup is one of my absolute favorites.  It's so flavorful, thick and hearty...  as my grandma used to say, it sticks to your ribs!  It's one of those great comfort foods that makes you smile during the cold winters.  The ham bone gives it deep, meaty flavor along with the earthiness of the bay leaf and the sweetness of the carrot and onion.  Very simple to make and very satisfying to eat.  I'll hope you'll give this one a shot!

1 ham bone (or substitute with 2 ham hocks or 2 strips of bacon or fatback, or leftover fat from the ham)
2 cups ham, diced into ½ pieces, fat and skin removed (use a little more or less to your liking)
1 medium onion, diced
1 carrot, peeled and shredded
1 lb. dry split peas, odd ones removed
7 cups water (for thinner soup, use 8 cups)
½ cup of half and half
1 bay leaf
1 tbsp. butter
1 tbsp. extra virgin olive oil
kosher salt and cracked black pepper to taste