Cook your rice if you have not already, instructions here. In a small bowl, whisk together the corn starch, 2 tablespoons soy sauce, and pepper until combined. Pour over the steak on your cutting board and toss to coat.
In a large skillet over medium-high heat, warm 1 tablespoon olive oil. Add the steak and spread out into an even layer. Let it cook for 3-5 minutes, undisturbed, or until pieces have a dark golden brown color on the bottom and are mostly cooked through. Give everything a stir, turn off the heat, then transfer to a plate or bowl.
To the skillet over medium heat, add the remaining olive oil along with the tomatoes, scallions, garlic, and salt. Cook for 2-4 minutes or until everything has softened and tomatoes have broken down a bit, stirring occasionally and scraping up any bits stuck to the bottom.
Add the beef back to the skillet along with the greens and cook for another minute, stirring frequently, or until the greens are wilted. Stir in the water and remaining 2 tablespoon soy sauce for 30 seconds, then turn off the heat.
Serve over warm rice and top with some black pepper and a squeeze of lime.