Season the steak with salt and pepper. In a medium bowl, whisk together the soy sauce, chile pepper, sugar and lime juice until the sugar is dissolved. Add the beef, toss to coat and set aside.
In a large skillet over medium-high heat, heat the oil until shimmering, about 1 minute. Add the beef and cook, stirring, until cooked through, 3 to 5 minutes.
Remove the beef from the skillet and set aside. Allow the liquid in the pan to reduce until thickened, about 4 minutes. Add the garlic and scallions and cook 1 minute more. Add the mushrooms and cook for 2 to 3 minutes more. Add the snow peas, baby corn and bell pepper and continue cooking until all the vegetables are crisp-tender, about 2 minutes. Return the beef to the skillet and toss to combine.