In medium-size saucepan, heat oil over medium-high heat. Add the bacon strips; cook, stirring occasionally, for 3 minutes or until the fat begins to render out of the bacon. Add the onion and sweet green pepper; cook, stirring occasionally, for 5 minutes or until the onion is softened.
Add rice to saucepan, stirring to coat the rice with the bacon fat. Add the broth, the 1/3 cup water, Cajun seasoning and salt. Bring to a boil over medium-high heat. Cover the saucepan. Reduce the heat to low; simmer 12 minutes or until the rice is almost tender and most of the liquid has been absorbed.
Add the drained black-eyed peas to the rice, stirring to evenly distribute; simmer, covered, for 3 minutes or until the rice is tender and all the liquid has been absorbed. Stir in the parsley until well mixed.
Serve the rice warm.