This is the simplest soup in the universe, and one of the most heart-warming when it's cold outside.
I try to keep its ingredients on hand all the time during the winter, so if a craving strikes, I can put it together without going shopping. If you buy the ham hocks two or three at a time, you can throw the extra(s) in the freezer. Of course if you happen to have a leftover ham bone, you can use that instead. Besides the ham and the split peas (which keep forever), all the ingredients are things a cook usually has on hand anyway: an onion, three or four carrots, a little olive oil.
And it smells so good while it's cooking.
Making it couldn't be easier. Just sauté diced onion and carrot in a little olive oil, add water, split peas and the ham hock, and let it simmer till it starts looking like soup. Take out the ham, discard its bone and fat, cut up the meat and toss it into the soup. Correct the seasoning and that's it – very little effort; time (about an hour and a half, maybe a little more) does all the work for you.
Start it in on a weekend morning, and you can eat it for lunch. Or make it in the afternoon and serve it on Monday or Tuesday night – with some good crusty dark rye bread and sweet butter, and maybe a salad – for a zero-effort dinner.