Senate bean soup (or: how to use up all that extra ham)

You bought a 15-pound ham a week ago, and have now made three dinners, five sandwiches, one pasta dish, and a couple of breakfasts from it, but you've still got a few pounds left. Don't you dare ponder throwing away those last few pounds of meat and bone: they're the perfect starting point for possibly the tastiest classic American soup.

Senate bean soup is apparently served daily in the US Senate restaurant, and it seems like there are a few dozen different versions of the recipe (including an official one on the Senate's website). My SO and I first found this recipe in Joy of Cooking, and have been happily making this soup ever since when we buy a ham. This soup is hearty and savory, and it makes great lunches or dinners on cold winter days. The soup also freezes well, so making a large batch can supply you with meals for months to come.

We made this soup last weekend, so it's this week's first end-of-the-week recipe blogging post.

4 cups dry navy beans
Leftover ham, including the bone (we used 5 pounds, including bone, of an approximately 12-pound ham)
22 cups water (not including water to soak the beans in)
3 carrots, peeled and sliced
3 stalks celery, with leaves, washed and sliced
4 large onions, diced
4 potatoes, washed and diced into ~3/8" cubes
8 cloves garlic, finely minced or pressed with a garlic press
1 1/2 teaspoons ground black pepper
Salt to taste (we used ~1 tablespoon kosher salt)

0) Cover the beans with at least 2" of water in a large bowl, and leave them to soak overnight in the fridge. If you're in a hurry, you can heat water to near boiling and pour it over the beans and soak for about an hour. If you're really in a hurry, you could probably get away without soaking the beans, and just increase the cooking time in step 1.
1) Drain the beans and put them in a large pot with the ham and water. If all the water doesn't fit in the pot initially, that's OK (as long as the ham and beans are covered). Bring to a boil and simmer until the beans are tender (~ 1 1/4 hours).
2) Remove the ham from the pot (caution: it's hot, and will be falling apart) and set it aside to cool.
3) Mash the beans slightly with a potato masher; this is optional, but makes the soup a bit creamier in texture.
4) Add the carrots, celery, onions, potatoes, and garlic.
5) Once the ham is cool enough to handle, remove the meat from the bone and cut into bite-sized pieces. Our ham often ends up very irregularly shaped (torn in some places, neat cubes in others), which adds a rustic note. If you left out any water above (in step 1), add it now.
6) Cook the soup for ~20 minutes, until the vegetables are soft.
7) Add the ham pieces and pepper, taste the soup, and adjust the salt level. If the ham pieces are cooler than you'd like, simmer the soup for a bit to heat them up.

Joy of Cooking recommends garnishing the soup with parsley.

Notes:

This recipe is scaled up to use a large amount of ham (and could probably feed the entire US Senate); if you have less ham (or want to buy a small ham hock), just scale down the recipe. Don't worry if you can't evenly divide the number of carrots and other vegetables if you scale the recipe; just pick a number and go with it.

The amounts (and even type) of ingredients in this recipe are relatively flexible. For instance, the original recipe omits carrots and uses more celery; we've made it both ways. We also rarely measure the amount of ham we use - we just take a ballpark guess and choose amounts of the other ingredients that seem to match. Sometimes the soup is extra hammy (as this version is), and sometimes it's more beany or vegetabley; it's always good.

Rombauer, I. S., M. R. Becker, and E. Becker. 1997. Joy of Cooking. Scribner, NY.