Pat the beef pieces dry and season lightly with salt and pepper. In a small bowl, combine the sauce ingredients, whisking to combine. Set aside.
In a 12-inch deep skillet or pot, heat the olive oil and sesame oil over medium or medium-high until hot and rippling. Cook the beef in a single layer until browned and mostly cooked through, 3-4 minutes. Repeat if all the beef didn't fit in the first batch. Remove the beef to a plate.
In the skillet or pot, add the ginger and garlic. If the pot is dry, drizzle in another teaspoon of oil. Cook over medium heat, stirring and mashing the ginger and garlic, for about 30 seconds until sizzling and fragrant (don't let it burn). Add the broccoli and broth.
Break the bricks of ramen noodles into chunks and add them to the skillet/pot. Bring the mixture to a simmer and cook until the ramen and broccoli are tender, 3-4 minutes, tossing and stirring the ramen while it cooks to help it separate. There should be a bit of liquid left in the bottom of the pot.
Add the beef back to the pot. Whisk the sauce to recombine and add it to the pot as well. Stir and toss the ingredients to combine. Cook at a gentle simmer for 1-2 minutes to heat through. Serve immediately.
Meat: I haven't tried it, but I think this meal would work quite well with ground beef in place of the flank or sirloin steak.Low-Sodium:using low-sodium broth and low-sodium soy sauce might be important if you are worried about the overall dish being too salty.Hoisin or Oyster Sauce Substitution: If you don't have hoisin or oyster sauce on hand, you can think outside the box a little and consider using ketchup or BBQ sauce. It will change the flavor profile, but can probably be used in a pinch for a thick, saucy substitution.