Trim excess fat off the flank steak, cut into 1 1/2 to 2-inch slices against the grain. Mix the baking soda, sugar, cornstarch, soy sauce, water, and oil in a bowl and whisk together. Add cut steak to a gallon sized zip lock bag and pour in the marinade. Massage the marinade into the meat so all of it is covered. Place in fridge and let marinate for 1 hour.
First, mix the "gravy" by placing the soy, stock, brown sugar, garlic, ginger, vinegar and flour into a small bowl, whisk to combine until there are no lumps of flour. Set aside.
In a large, heavy bottom skillet, heat over high temp until very hot. Place 2 Tablespoons of the oil into skillet. Place broccoli into the oil, very carefully (make sure broccoli is COMPLETELY dry or you will get hot oil splattered all over). Saute broccoli for 3 minutes, stirring occasionally. Place broccoli on a plate and set aside.