Heat the vegetable oil in a large pot or Dutch oven over medium-high heat.
Add the sliced beef and cook until browned on all sides, about 3 to 4 minutes. Remove the beef from the pot and set it aside.
Reduce the heat to medium. Add the minced garlic and grated ginger to the pot and cook for 30 seconds until fragrant.
Pour in the beef broth, soy sauce, brown sugar, and rice vinegar. Bring the liquid to a boil.
Add the ramen noodles and broccoli florets to the boiling broth. Cook, stirring occasionally, until the noodles soften and the broccoli is tender-crisp, about 3 to 5 minutes.
Return the cooked beef to the pot. Stir in the sesame oil.
If using eggs, crack them directly into the simmering broth around the noodles. Cover the pot and cook for 3 to 4 minutes for soft-set yolks.
Divide the ramen, beef, and broccoli into bowls. Top with the cooked eggs, if desired. Serve immediately.
Notes
Use flank steak or sirloin cut against the grain for the best texture.
For a thicker sauce, mix 1 teaspoon of cornstarch with 2 teaspoons of cold water before adding it in step 5.
If you skip the eggs, you can add a sprinkle of sesame seeds or chopped green onions as a garnish.