Wash and sort the peas. Place them in the saucepan, add the water, and discard debree and any peas that float. Gently boil the peas with the pepper, ham hock, and onion, uncovered, until tender but not mushy — about 1½ hours — or until 2 cups of liquid remain. Add the rice to the pot, cover, and simmer over low heat for about 20 minutes, never lifting the lid.

Remove from the heat and allow to steam, still covered, for another 10 minutes. Remove the cover, fluff with a fork, and serve immediately.