Step 1

Preheat oven to 400°F. In a dry large skillet over medium-high heat, cook onion and mushrooms with 1 teaspoon salt, stirring occasionally, until mushrooms release their moisture, 6 to 8 minutes. Add 1 tablespoon oil and beef. Cook, stirring and breaking up meat, until no longer pink but not cooked through, about 3 minutes.

Step 2

In a bowl, whisk together cornstarch, Worcestershire, and 2/3 cup water. Stir into skillet with frozen vegetables. Cook until vegetables are just thawed, about 1 minute. Season to taste; transfer to a shallow 2-quart baking dish. Top with cheese.

Step 3

Toss potatoes with remaining 2 tablespoons oil; season generously with salt and sprinkle over beef mixture. Bake until bubbly, about 40 minutes. Switch oven to broiler; broil until potatoes are golden brown in spots, about 5 minutes. Let cool 10 minutes; serve.