Place 1 3/4 cups dried black-eyed peas in a colander and rinse under cold water.
In a large Dutch oven, cook 4 slices bacon, diced, over medium heat until crisp, 8 minutes. Remove bacon with slotted spoon. Set aside. Add 1 medium onion, chopped, to drippings; cook 5 minutes or until tender. Stir in black-eyed peas, bacon, 4 cups water, 8 ounces diced ham, 1/4 tsp cayenne, and 1/8 tsp black pepper. Bring to a boil; reduce heat. Simmer, covered, for 20 minutes. Stir in 3/4 cup uncooked converted long-grain white rice. Return to boiling; reduce heat. Simmer, covered, for 15 minutes. Remove from heat. Let mixture stand, covered, for 10 minutes. Stir in 3 chopped scallions before serving.