In a small bowl, mix soy sauce, vinegar, peanut butter, honey, and garlic; season with pepper.
In a bowl, toss steak with cornstarch; season with salt and pepper. In a large nonstick skillet with a lid, heat oil over medium-high. Add 1/2 of steak; cook, tossing, until browned, 1 to 2 minutes. Transfer to a plate; repeat with remaining steak.
To skillet, add soy mixture, bok choy, and carrots. Cover and cook, tossing occasionally until tender, about 5 minutes. Return steak to skillet; cook until heated through, about 5 minutes. Serve over rice; sprinkle with peanuts.