Cut the pork tenderloin widthwise into 1/4-inch-thick rounds.
In a large bowl, whisk together 1/4 cup soy sauce, garlic powder and black pepper. Add the sliced pork and toss to combine. Let stand at room temperature for 10 minutes.
Heat a large skillet over high heat. Add 2 tablespoons vegetable oil and swirl to coat the pan. Arrange half of the pork in a single layer. Cook the pork, flipping once, until it is browned on both sides and cooked through, 3 to 5 minutes. Using a slotted spoon, transfer the pork to a plate and repeat the cooking process with the remaining pork, transferring it to the plate. (If needed, add an additional 1 tablespoon vegetable oil to the skillet.)
Reduce the heat to medium and add the remaining 1 tablespoon vegetable oil to the skillet. Add the broccoli florets and cook, stirring, until it is crisp-tender, about 3 minutes. (See Kelly’s Note.) Transfer the broccoli to the plate with the pork.
Add the remaining 1/4 cup soy sauce along with the brown sugar and cornstarch mixture to the skillet, stirring to remove any brown bits from the bottom. Bring the mixture to a boil and cook until thick and syrupy, about 2 minutes.
Return the pork and broccoli to the skillet and toss to coat. Garnish with sesame seeds and serve.