Make the stir-fry sauce by whisking all the ingredients together in a medium bowl. Set aside.
Heat a large cast-iron skillet over medium-high heat. When the skillet is very hot, melt two tablespoons of tallow.
Salt and pepper the beef, then add it to the hot pan and sear, 2 to 4 minutes on each side, until slightly undercooked to your preference. Set aside on a cutting board and let it rest for 15 minutes before slicing it thin.
While the meat rests, reduce the skillet’s heat to medium and add the broccoli and onion.
Sauté, stirring occasionally, until the broccoli is softened and the onion has started to caramelize.
Return the sliced beef to the skillet and pour the stir-fry sauce over the beef and broccoli. Simmer and stir until thickened.
Serve hot over rice, garnished if desired.