Set a large skillet, pan, pot, or Dutch oven over medium-high heat. Add the ground beef and cook until no longer pink, breaking apart and stirring as the meat cooks. Drain the grease from the pot; add the rice, beef broth, soy sauce, oyster sauce, garlic powder, and pepper, and stir well to combine. Increase heat to high and bring to a boil, then stir and reduce to a simmer. Simmer, covered, for 10 minutes, stirring occasionally. Stir in shredded carrots and continue to cook for 5 to 10 more minutes, stirring occasionally, until rice and carrots are tender and the liquid is mostly absorbed. Stir in the thawed peas and cook for another minute until heated through.
If you don't have oyster sauce, you may omit it, but I always keep a bottle in my fridge because I think it adds great depth of flavor to Asian recipes. If you don't include it in this recipe, you might find that you need to stir in a bit more soy sauce (to taste) at the end of the cooking time.
To quickly thaw my frozen peas, I place them in a colander and run them under hot tap water for a minute.
When you bring the mixture to a boil and reduce to a simmer, make sure that the simmer is a simmer...not barely bubbling (or the rice won't cook and absorb the liquid) and not bubbling too fast (or the liquid may get absorbed too fast and the bottom may burn). For my stove, this was medium-low heat, adjusting up or down a tad as needed when I would stir every few minutes.
If too much liquid remains once your rice is cooked, you may remove the lid and turn up the heat for a minute or two, stirring so that it doesn't burn. If the liquid evaporates before the rice is done and everything starts to stick to the bottom, you may stir in a bit more broth or water.