Slice and velvet the beef: Cut the partially frozen beef across the grain into thin strips, about ¼-inch thick. In a bowl, toss the beef with the baking soda, 1 tablespoon of the soy sauce, 1 teaspoon of the cornstarch, and 1 teaspoon of the sesame oil. Let it sit at room temperature for 10 minutes.
Make the sauce: In a small bowl, whisk together the remaining soy sauce, brown sugar, grated ginger, minced garlic, remaining sesame oil, remaining cornstarch, and ¼ cup of water. Set it near the stove. Give it another whisk right before using.
Par-cook the broccoli: Heat a teaspoon of neutral oil in your skillet over medium-high. Add the broccoli florets and let them sit undisturbed for 2 minutes until the undersides char. Toss and cook for 1 more minute until bright green and crisp-tender. Transfer to a plate.
Sear the beef: Add another tablespoon of neutral oil to the skillet and turn the heat to high. Spread the beef in a single layer. Cook for 45 seconds to 1 minute without moving it, then toss and cook for another 30 seconds. It will still be slightly pink – that's fine. Transfer to the plate with the broccoli.
Optional aromatics: Add 2 more minced garlic cloves and a pinch of red pepper flakes to the hot pan for about 15 seconds.
Simmer the sauce: Pour the sauce mixture into the hot skillet. Stir constantly until it thickens and becomes glossy, about 45 seconds. When you can drag a spoon through and it leaves a clean trail, it's ready.
Combine everything: Return the beef and broccoli to the skillet. Toss together until evenly coated, about 30 seconds.
Serve immediately over hot rice. The whole process takes about 25-30 minutes.