Start by boiling the ramen noodles in a pot of water for about 3 minutes or according to the package directions. Drain and rinse under cold water to stop the cooking process.
In a small bowl or measuring cup, combine the grated ginger, garlic, soy sauce, warm water, brown sugar, cornstarch, sesame oil, and black pepper. Stir well until the sugar dissolves and the mixture is smooth.
Heat half the oil in the skillet over medium heat. Add the broccoli and a splash of water, cover, and steam for about 4 minutes until crisp-tender. Remove from the pan and set aside.
Increase the heat to medium-high and add the remaining oil. Add the thinly sliced beef in a single layer and cook about 2 minutes per side until just browned and cooked through.
Give your sauce a quick stir, then pour it into the pan with the beef. Let it simmer for 3-4 minutes until it thickens. Return the broccoli and add the drained ramen noodles. Toss everything together until the noodles are coated in the sauce and everything is heated through. Thin the sauce with a splash of water if needed.