Heat the olive oil in a large pot over medium-high heat until it shimmers. Add the onions and fennel and cook until soft.
Drain the crowder peas and add them to the pot. Add six cups of fresh cold water, plus all the ingredients through the brown sugar. Bring the pot to a boil, then lower to a simmer. Cover and cook for one hour.
Check after an hour to see that the peas have not absorbed all the water. If so, add more. The pot should still have a soup texture at this point.
Cook another 30-45 minutes, until beans are soft but still in one piece. Remove the bay leaf. Taste for seasoning and adjust. There should still be enough liquid so that the beans have a stew-like texture.
Add the cooked, drained rice to the pot and gently stir into the beans. Serve garnished with fresh chopped parsley.