Preheat oven to 350 degrees F (175 degrees C). Bring a saucepan of salted water to a boil. Break each ramen noodle block into 4 pieces and cook, stirring occasionally, until just tender, about 3 minutes. Drain noodles in a colander and rinse under cold water.

Heat 1 tablespoon oil in a 12-inch nonstick skillet (with lid) over medium-high heat until shimmering. Spread noodles evenly to cover bottom of skillet. Cook noodles, pressing on them occasionally with a slotted spatula, until underside is golden brown, 3 to 6 minutes. Slide ramen cake onto a large plate, invert a second plate over top, then flip cake over (so cooked side is now on top). Add remaining tablespoon oil to skillet. Slide ramen cake back into skillet and cook over medium-high heat, pressing it occasionally, until underside is golden brown, 3 to 5 minutes. Slide ramen cake onto a baking sheet and keep warm in oven (do not clean skillet).

While ramen cake cooks, whisk together water, oyster sauce, soy sauce, cornstarch, sugar, and sesame oil (if using).

Heat 1 tablespoon oil in same skillet over medium-high heat until shimmering. Add broccoli and stir-fry 1 minute. Add water and cook, covered, over medium heat until crisp-tender, 2 to 3 minutes. Transfer broccoli to a bowl and wipe out skillet.

Heat remaining 1 1/2 tablespoons oil in skillet over medium-high heat until shimmering. Stir-fry garlic and ginger 10 seconds. Add beef and salt and stir-fry until beef is browned, about 2 minutes.

Stir sauce, then add to skillet and bring to a boil, stirring. Add broccoli and cook, stirring, until heated through, about 30 seconds. Remove from heat.

Slide ramen cake onto a cutting board and cut into quarters. Top each ramen wedge with 1 cup beef-broccoli mixture.