Bring the rice and water to a boil in a saucepan over high heat. Reduce heat to medium-low, cover, and simmer until the rice is tender, and the liquid has been absorbed, 20 to 25 minutes.
Meanwhile, heat the olive oil in a large skillet over medium heat. Stir in the carrots, celery, garlic, and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in the black beans, salt, pepper, 1/4 cup of parsley, and dark rum. Continue cooking until heated through. Serve over a bed of rice and garnish with 1 teaspoon of parsley.