In a large bowl or in a large Ziploc bag, stir together the steak, 1 tablespoon of soy sauce, 1 tablespoon of rice vinegar, and 1 tablespoon of sesame oil. Cover and refrigerate for 1 hour (or up to overnight).
In a small bowl or large measuring cup, whisk together the cornstarch and the remaining 3 tablespoons of soy sauce until smooth. Add the broth, remaining 1 teaspoon of rice vinegar, remaining 1 teaspoon of sesame oil, brown sugar, kosher salt, and black pepper. Whisk to combine. Set aside.
Remove the steak from the marinade; set it on a plate. If there’s any extra marinade left in the bag or bowl, add it to the broth mixture.
Heat 1 tablespoon of vegetable oil in a wok or large skillet (at least 12-14 inches) over medium-high heat. Add the steak in a single layer; cook until browned, about 5-6 minutes. Remove the steak to a clean plate. Wipe out the skillet, discarding the drippings.
Reduce the heat to medium. Add the remaining 1 tablespoon of vegetable oil. When the oil is hot, add the bell peppers and onion. Cook, stirring occasionally, until the vegetables are lightly browned, about 5-6 minutes. Add the garlic and ginger; cook, stirring constantly, for 2 more minutes.
Add the steak and sauce to the skillet. Cook, stirring constantly, until the sauce thickens, about 3-5 minutes. Remove from the heat.
Serve with rice and garnish with green onion, sesame seeds, or crushed red pepper flakes.