Prepare the Carrot: Peel the carrot and cut it lengthwise into 1/2-inch-thick slices, then stack the slices and cut them into thin strips.
Slice the Pepper: Remove the top of the red bell pepper, separate the flesh from the white core and membranes, discard the core and membranes, and cut the pepper into thin strips.
Prepare the Aromatics: Peel and finely grate the fresh ginger and garlic, then set them aside.
Slice the Beef: Cut the flank steak across the grain into thin slices approximately 1/4 inch thick.
Coat the Beef: Place the sliced flank steak and cornstarch in a large Ziploc bag, seal it, and shake thoroughly until the beef is evenly coated.
Heat the Pan: Place a large skillet or wok over medium-high heat and allow it to heat before adding the oil.
Cook the Vegetables: Add 1 tablespoon of the oil, followed by the carrot, green onions, and red bell pepper. Sauté for 2–3 minutes, stirring frequently, until the vegetables are crisp-tender. Mix the Sauce: While the vegetables cook, combine the grated ginger, honey, grated garlic, water, low-sodium soy sauce, and Sriracha in a bowl. Whisk until well combined, then set aside. Remove the Vegetables: Transfer the sautéed vegetables from the skillet or wok to a plate or bowl and set them aside.
Heat the Remaining Oil: Add the remaining 1 tablespoon of oil to the hot skillet or wok and heat until the oil is hot.
Sear the Beef: Add the cornstarch-coated beef to the hot oil and sauté for about 2 minutes, turning and stirring as needed, until the beef is seared on all sides but still barely cooked in the center.
Combine the Ingredients: Return the sautéed vegetables to the skillet or wok, then pour in the prepared sauce. Mix thoroughly so the beef and vegetables are evenly coated. Thicken the Sauce: Continue cooking for about 3 minutes, stirring regularly, until the sauce thickens and coats the beef and vegetables.
Serve Immediately: Serve the Mongolian Beef Stir Fry immediately with steamed jasmine rice and a sprinkle of sesame seeds, if desired.