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In a medium bowl, whisk soy sauce, vinegar, brown sugar, and cornstarch until combined.
In a large skillet over high heat, heat 1 tablespoon oil. Working in batches, add steak; season with salt and pepper. Cook, turning occasionally, until browned on all sides, about 8 minutes total. Transfer steak to a plate.
In same skillet over medium heat, heat remaining 1 tablespoon oil. Cook bell peppers, stirring occasionally, until softened, about 5 minutes. Add garlic and ginger and cook, stirring, until fragrant, about 1 minute more. Return beef to skillet and add sauce; season with salt and pepper, if needed. Cook, stirring, until sauce is glossy, about 2 minutes more.
Divide rice among plates. Spoon steak mixture over.