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.
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).
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.