In a small bowl, stir together the soy sauce, brown sugar, garlic, flour, and sherry until smooth. Set aside.
In a large wok or sauté pan, heat 2 tablespoons of the vegetable oil over high heat until shimmering. Add broccoli and sauté for three minutes, stirring often. Transfer broccoli to a plate.
Reduce heat to medium high. Carefully add the remaining tablespoon of vegetable oil to the hot pan.
Add the marinaded meat and half of the sauce mixture and sauté for three to four minutes, stirring often, until the meat is cooked through and no longer pink.
Stir in the broccoli and remaining sauce. Sauté one minute more. Serve.