Combine the sirloin pieces with 1 tablespoon soy sauce and 1/2 teaspoon black pepper in a bowl; stir to coat and set aside to marinate while you prepare the sauce and vegetables.
Make the sauce by whisking together 1/3 cup soy sauce, 1/4 cup water, 3 tablespoons maple syrup, 1 tablespoon rice vinegar, 1 tablespoon minced garlic, 1 tablespoon minced ginger, 1/4 teaspoon red pepper flakes, and 1 tablespoon cornstarch until smooth; set aside.
Heat a large deep sauté pan or wok over medium-high heat and add 1/2 tablespoon oil. When hot, add the marinated beef in a single layer and cook, stirring or tossing, until browned and cooked through, about 3–5 minutes. Transfer the beef and any accumulated juices to a plate.
Add the remaining 1/2 tablespoon oil to the pan. Add the sliced red bell pepper and the chopped mixed vegetables; stir-fry until they are slightly softened and lightly browned, about 3–4 minutes.
Return the cooked beef and any juices to the pan and add the drained water chestnuts. Pour the prepared sauce over everything and toss to combine.
Cook and stir for 3–4 minutes, allowing the sauce to thicken and the ingredients to heat through. Stir in about half of the chopped green onions.
Transfer to a serving platter or bowls and sprinkle with sesame seeds and the remaining green onions. Serve warm over rice, quinoa, noodles, or cauliflower rice.
