Heat the vegetable oil in a large skillet over medium-high heat.
Add the ground beef to the skillet and cook, breaking it up with a spatula, until browned and cooked through, about 5 minutes.
Add the diced onion and minced garlic to the skillet with the beef. Cook, stirring occasionally, until the onion is softened, about 3 minutes.
Pour in the beef broth, soy sauce, brown sugar, sesame oil, and black pepper. Stir to combine.
Add the shredded carrots and chopped green cabbage to the skillet. Stir and cook for 2 minutes until the vegetables begin to soften.
Break the ramen noodles into smaller pieces and add them to the skillet. Stir to submerge the noodles in the liquid.
Cover the skillet with a lid and let cook for 3 to 4 minutes, or until the noodles are tender and most of the liquid is absorbed.
Remove the lid and stir the mixture to combine everything evenly.
Sprinkle the sliced green onions on top before serving.