Steps:
- 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.
- Put oven rack in middle position and preheat oven to 400°F.
- While soup simmers, toss bread with remaining 3 tablespoons oil and kosher salt in a large bowl, then spread in 1 layer in a large shallow baking pan and bake until crisp, about 10 minutes. Cool croutons in pan on a rack.
- 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. Add frozen peas and simmer, uncovered, stirring, until just heated through, about 3 minutes. Season with salt.
- Serve soup with croutons.
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