Whisk together the baking soda, sugar, cornstarch, soy sauce, water, and vegetable oil in a large bowl.
Toss the steak with the marinade to coat.
Cover and refrigerate at least 1 hour.
In a small bowl, stir together the 1/2 cup soy sauce, brown sugar, garlic, flour, and sherry until smooth. Set aside.
In a large wok or saute pan, heat 2 tablespoons of the vegetable oil over high heat until shimmering. Add broccoli and saute 3 minutes, stirring often. Transfer broccoli to a plate.
Reduce heat to medium-high. Carefully add the remaining tablespoon of oil to the hot pan. Add the marinated meat and half of the sauce mixture and saute for 3-4 minutes, stirring often, until the meat is cooked through and no longer pink.
Stir in the broccoli and remaining sauce. Saute 1 minute more. Serve with rice.