For the sauce: Whisk all ingredients together in a bowl.
For the beef: combine soy sauce and rice wine (sake) in a bowl, stir in the beef, and marinate for at least 10 minutes or up to 1 hour.
For the stir-fry: combine the scallions, garlic, ginger and 1 tsp of the canola oil in a bowl.
Heat 2 tsp more canola oil in a 12-inch nonstick skillet over high heat until just smoking. Add the beef, break up any clumps, and cook until lightly browned on all sides but not fully cooked, about 2 minutes. Transfer to a bowl, cover, and set aside.
Add the remaining tsp canola oil to the skillet and return to high heat until shimmering. Stir in the broccoli, add the water, cover, and steam until broccoli is bright green and begins to soften, about 2 minutes.
Uncover and allow the water to evaporate, 30 to 60 seconds. Stir in the bell peppers and cook until the vegetables are crisp-tender, 3 to 4 minutes.
7. Clear the center of the skillet, add the garlic mixture, and cook, mashing the mixture into the pan, until fragrant, 15 to 30 seconds. Stir it into the vegetables.
8. Return the beef, with any accumulated juice, to the skillet. Whisk the sauce to recombine, then add to the skillet. Simmer, tossing constantly, until the beef is cooked through and the sauce has thickened, 30 seconds to 2 minutes. Serve.