Place the thinly sliced beef in a bowl and add 1 tablespoon of the soy sauce, half of the minced garlic, and half of the grated ginger. Toss to coat and let stand while you prepare the vegetables.

In a small bowl, whisk together the remaining 2 tablespoons soy sauce, hoisin sauce, sesame oil, honey, and the remaining garlic and ginger until smooth. Set the sauce aside.

Prep the vegetables by slicing the bell pepper, cutting the broccoli into small florets, julienning the carrot, and trimming the snap peas. Chop the green onions and set aside for garnish.

Heat a large skillet or wok over medium high heat until hot. Add 1 tablespoon vegetable oil and swirl to coat the pan.

Add the marinated beef in a single layer, cooking in batches if needed. Stir fry for 2 to 3 minutes until mostly browned but still tender. Transfer the beef to a plate and set aside.

Add the remaining 1 tablespoon vegetable oil to the same pan. Add the carrot, bell pepper, and broccoli. Stir fry for 3 to 5 minutes until the vegetables brighten in color and are crisp tender.

Add the snap peas to the pan and stir fry for 2 to 3 minutes until they are bright green and just tender.

Return the cooked beef and any juices to the pan. Pour in the prepared sauce and toss everything together until the beef and vegetables are evenly coated.

Let the stir fry cook for 1 to 2 minutes, stirring often, until the sauce bubbles and thickens slightly and clings to the beef and vegetables.

Remove from the heat. Sprinkle with chopped green onions and sesame seeds. Serve hot over steamed rice.