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1.
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Toss beef with 2 tablespoons water, 1 teaspoon salt, 1/4 teaspoon pepper, and baking soda in bowl until thoroughly combined.
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Set aside for 20 minutes.
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2.
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Meanwhile, place potatoes in medium saucepan; add water to just cover and 1 tablespoon salt.
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Bring to boil over high heat.
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Reduce heat to medium-low and simmer until potatoes are soft and tip of paring knife inserted into potato meets no resistance, 8 to 10 minutes.
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Drain potatoes and return to saucepan.
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Return saucepan to low heat and cook, shaking pot occasionally, until any surface moisture on potatoes has evaporated, about 1 minute.
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Remove pan from heat and mash potatoes well.
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Stir in melted butter.
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Whisk together milk and egg yolk in small bowl, then stir into potatoes.
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Stir in scallion greens and season with salt and pepper to taste.
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Cover and set aside.
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3.
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Heat oil in broiler-safe 10-inch skillet over medium heat until shimmering.
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Add onion, mushrooms, 1/2 teaspoon salt, and 1/4 teaspoon pepper; cook, stirring occasionally, until vegetables are just starting to soften and dark bits form on bottom of skillet, 4 to 6 minutes.
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Stir in tomato paste and garlic; cook until bottom of skillet is dark brown, about 2 minutes.
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Add Madeira and cook, scraping up any browned bits, until evaporated, about 1 minute.
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Stir in flour and cook for 1 minute.
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Add broth, Worcestershire, thyme, bay leaf, and carrots; bring to boil, scraping up any browned bits.
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Reduce heat to medium-low, add beef in 2-inch chunks to broth, and bring to gentle simmer.
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Cover and cook until beef is cooked through, 10 to 12 minutes, stirring and breaking up meat chunks with 2 forks halfway through.
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Stir cornstarch and remaining 2 teaspoons water together in bowl.
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Stir cornstarch mixture into filling and continue to simmer for 30 seconds.
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Remove thyme and bay leaf.
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Season with salt and pepper to taste.
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4.
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Adjust oven rack 5 inches from broiler element and heat broiler.
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Place mashed potatoes in large zipper-lock bag and snip off 1 corner to create 1-inch opening.
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Pipe potatoes in even layer over filling, making sure to cover entire surface.
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Smooth potatoes with back of spoon, then use tines of fork to make ridges over surface.
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Place skillet on rimmed baking sheet and broil until potatoes are golden brown and crusty and filling is bubbly, 10 to 15 minutes.
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Let cool for 10 minutes before serving.
