Cook the barley as the label directs. Cover and set aside.
Meanwhile, whisk 1 tablespoon Worcestershire sauce with 2 teaspoons brown sugar in a medium bowl. Add the pork, season with salt and pepper and toss to coat. Whisk the chicken broth, cornstarch and the remaining 1 teaspoon Worcestershire sauce and 2 teaspoons brown sugar in a small bowl until smooth; set aside.
Heat 1 tablespoon vegetable oil in a large nonstick skillet over high heat. Add the pork and cook, turning occasionally, until well browned, about 4 minutes. Remove to a plate.
Wipe out the skillet and add the remaining 1 tablespoon vegetable oil. Add the mushrooms, leeks, carrots, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the vegetables are tender, about 4 minutes. Return the pork to the skillet and add the broth mixture. Cook, stirring, until the sauce is slightly thickened, 1 to 2 minutes. Serve with the barley; top with parsley.