Toss the beef with 1/2 teaspoon of the cornstarch, 1/2 teaspoon salt and 1/8 teaspoon pepper in a medium bowl. Rest at room temperature for 15 minutes.
Put the potatoes and 1 teaspoon salt in a large skillet and cover with 2 cups water. Bring to a simmer and cook until tender, about 4 minutes. Drain the potatoes and set aside. Rinse the skillet and wipe dry.
Whisk together the broth, soy sauce, 1/4 teaspoon salt and the remaining 1 teaspoon cornstarch in a small bowl until the cornstarch dissolves. Set aside.
Put the reserved skillet over medium-high heat and heat 1 tablespoon of the oil. Add the mushrooms in 1 layer, season with salt and pepper and cook without stirring until the mushrooms are nicely browned on the bottom, 2 to 3 minutes; transfer to a large bowl. Add 1 tablespoon plus 1 teaspoon of the oil to the skillet, then add the beef in a single layer. Cook without stirring until browned on one side but not completely cooked through, about 1 minute. Transfer to the bowl with the mushrooms.
Add the remaining 1 tablespoon oil to the skillet, then add the carrots and celery. Season with salt and pepper. Cook, stirring, for about 1 minute, then add the garlic and cook for 30 seconds. Add the tomato paste and cook, stirring continuously, until it turns a shade darker, about 30 seconds. Pour in the beef stock mixture, making sure all of the cornstarch is incorporated. Return the beef, mushrooms and potatoes to the skillet. Simmer until the sauce thickens and the flavors are blended, about 2 minutes. Adjust the seasoning if necessary. Remove from the heat and stir in the butter, parsley and scallions.
Serve with buttered egg noodles or mashed potatoes and sprinkle with additional sliced scallions.
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