Christina's Split Pea Soup

2 meaty ham hocks (1 3/4 lb total)
16 cups water
4 large carrots
1 large onion, chopped
2 celery ribs, chopped
5 tablespoons olive oil
1 lb dried split peas (2 1/4 cups), picked over and rinsed
1 teaspoon table salt
1/4 teaspoon black pepper

Simmer ham hocks in 16 cups water in a deep 6-quart pot, uncovered, until meat is tender, 1 1/2 to 2 hours.
Transfer ham hocks to a cutting board and measure broth: If it measures more than 12 cups, continue boiling until reduced; if less, add enough water to total 12 cups. When hocks are cool enough to handle, discard skin and cut meat into 1/4-inch pieces (reserve bones).

Chop 2 carrots and cook along with onion and celery in 2 tablespoons oil in a 6- to 8-quart heavy pot over moderate heat, stirring, until softened, 6 to 8 minutes. Add split peas, table salt, pepper, ham hock broth, and reserved bones and simmer, uncovered, stirring occasionally, until peas are falling apart and soup is slightly thickened, about 1 1/2 hours.

Halve remaining 2 carrots lengthwise, then cut crosswise into 1/4-inch-thick slices. Remove bones from soup with a slotted spoon and discard. Add carrots and ham pieces to soup and simmer, uncovered, until carrots are tender, 10 to 15 minutes. Season with salt.