Brown the ground beef in a large pot or Dutch oven over medium-high heat. Drain off any excess fat.
Add the minced garlic and grated ginger to the pot with the beef. Cook for 1 minute until fragrant.
Add the broccoli florets and beef broth to the pot. Bring the mixture to a boil.
Once boiling, reduce the heat to medium-low, cover, and simmer for 5 minutes, or until the broccoli is tender-crisp.
Stir together the soy sauce and brown sugar in a small bowl. Pour this mixture into the pot.
In a separate small bowl, whisk together the cornstarch and 2 tablespoons of water to create a slurry. Pour the slurry into the simmering liquid while stirring constantly until the sauce thickens slightly.
Break the ramen noodle blocks into pieces and add them directly to the pot. Cook for 2 to 3 minutes, stirring occasionally, until the noodles are tender.
Remove from heat and serve immediately directly from the pot.
Notes
You can substitute thinly sliced flank steak for ground beef if desired; cook the steak first until browned, then remove it and add it back in with the noodles.
For a richer flavor, use low-sodium soy sauce.
If you prefer softer broccoli, simmer it for an extra 2 minutes before adding the noodles.