1. Try not to include little hambones easily mistaken for potato chunks.
2. Use a waxy variety potato next time; Russet turned a skosh mealy.
3. Add a chopped carrot along with said waxy potato, post blender.
4. Take Cook's Illustrated's advice and use ham steak instead of ham hock - I don't really enjoy the scent of bone in my soup. Plus some of the meat that comes off a hock is pretty nasty.
Here is the recipe for my concoction. I just had some for lunch with a 1/2 a grilled cheese, and you should, too.
Split Pea Soup a la Porkchop
adapted from several sources
1 C chopped onion
1/2 C chopped carrot
1/2 C chopped celery
2 T butter
1.5 LB smoked ham hock
1.5 C split peas, rinsed and checked for rocks
2 t dried marjoram (or 1 t thyme and 1 t oregano)
1 bay leaf
8 C water
1 chunked up potato
1 chunked up carrot
1/2 C leftover mashed potatoes (optional)
salt and pepper
In a large enough soup pot, melt the butter over medium heat. Add the chopped veg and sweat until soft,maybe 10 minutes. Add the ham hock, peas and herbs and stir. After a minute or so, cover with the water. Bring to a boil and simmer, stirring occasionally, until the ham is falling off the bone and the peas are mushy. A little over an hour, in my case.
Remove the ham to a cutting board and find the stupid bay leaf - remove it, too. Take half of the soup and either blend in batches in the blender or use a hand blender to puree until bright green and smooth. Return to pot with the unblended half. Add your chunked up veg and the mashed potatoes (if using) and continue to simmer until the potatoes are cooked through. In the meantime salvage what ham you can off the hock and return it to the pot as well. Taste and season with S&P.
I would recommend making this the day before you actually want to eat it - it tastes best if you refrigerate it overnight and reheat it the next day. Makes about 10 cups of soup.