In a medium saucepan, combine the rice and 3 cups water. Bring to a simmer, cover and cook over medium-low heat until the water is absorbed, about 20 minutes. Remove from the heat and let stand, covered, for 5 minutes before fluffing with a fork.
While the rice is cooking, in a large pot, heat 2 tablespoons olive oil over medium-high heat. Season the beef with salt and pepper. Working in batches, add the beef and cook until browned, about 2 minutes; transfer to a bowl. Lower the heat to medium, add the onion and remaining 1 tablespoon olive oil to the pot and cook until translucent, 3 to 4 minutes. Stir in the tomatoes, okra and beef broth; bring to a boil, stirring occasionally, then lower the heat and simmer until thickened, about 15 minutes. Return the beef and any juices to the pot and stir in the parsley. Serve with the rice.