Start by thinly slicing the flank steak against the grain. Place the sliced beef in a bowl and sprinkle with corn starch, tossing to coat evenly. Let it sit for about 10 minutes while you gather the other ingredients.
In a large skillet or wok, heat 1 tablespoon of the neutral oil over medium-high heat. Once hot, add the beef in a single layer. Cook for 2-3 minutes on each side until browned and crispy. Remove and set aside.
In the same skillet, add the remaining tablespoon of oil and the unsalted butter. Once melted, toss in the carrot and bell pepper. Sauté for 3-4 minutes until tender but still crisp.
Add the garlic, ginger, brown sugar, soy sauce, water, and Sriracha to the skillet. Stir well and bring to a simmer. Cook until the sauce thickens slightly.
Return the cooked beef to the skillet, stirring to coat in the sauce. Add the green onions and heat everything through for another minute.
Transfer the Mongolian beef to a serving platter and garnish with sesame seeds if using. Serve hot over steamed rice or noodles.