Step 1: Prepare the Beef. In a medium bowl, combine the thinly sliced beef with 1/4 cup of the soy sauce, 1 tablespoon of the cornstarch, and 1 teaspoon of the sesame oil. Mix well to coat the beef evenly. Let it marinate for at least 15 minutes, or up to 30 minutes, while you prepare other ingredients.
Step 2: Whisk the Sauce. In a small bowl, whisk together the remaining 1/4 cup soy sauce, 2 tablespoons rice vinegar, 1 tablespoon brown sugar, 1 teaspoon fresh grated ginger, 2 cloves minced garlic, the remaining 1 teaspoon sesame oil, and the remaining 1 tablespoon cornstarch. Set aside.
Step 3: Cook the Beef. Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat until shimmering. Add the marinated beef in a single layer, ensuring not to overcrowd the pan. Cook for 2-3 minutes per side, until browned. You may need to do this in two batches to ensure proper searing. Remove the beef from the skillet and set aside.
Step 4: Sauté the Vegetables. Add the remaining 1 tablespoon vegetable oil to the same skillet. Add the sliced yellow onion and cook for 2-3 minutes until slightly softened. Then, add the green, red, and yellow bell pepper strips and cook for an additional 3-5 minutes, stirring occasionally, until they are crisp-tender.
Step 5: Combine and Thicken. Return the cooked beef to the skillet with the vegetables. Give the whisked sauce from Step 2 another quick stir (cornstarch tends to settle) and pour it over the beef and vegetables. Bring the mixture to a simmer, stirring gently, and cook for 1-2 minutes until the sauce thickens and becomes glossy.
Step 6: Serve Immediately. Remove the skillet from the heat. Garnish with chopped green onions and a sprinkle of sesame seeds, if desired. Serve your Classic Skillet Pepper Steak hot over steamed white rice or noodles.