Prep the beef. Mix beef with water, salt, pepper, and baking soda in bowl until thoroughly combined. Set aside for 15-20 minutes.
Make the potato topping. Add potatoes to a medium pot, then add water to just cover the potatoes and 1/2 tbsp salt. Bring to boil over high heat, then reduce heat to medium-low and simmer until potatoes are soft and fork tender, about 8 to 10 minutes. Remove the potatoes to a strainer, reserving the water in the pot.
Return the pot of water to a boil, then add cauliflower florets. Boil for 10 minutes or until fork tender, then drain the water and return the cauliflower to the pot. Add half of the melted butter, then blend with an immersion blender until smooth. Note: you could use the immersion blender for both the cauliflower and the potatoes, but you risk creating gummy mashed potatoes.
Return potatoes to the pot with the cauliflower and add remaining melted butter and baking soda. In a small bowl, whisk half and half and egg yolk, then mix into potatoes. Stir in green onions and season with salt and pepper to taste. Cover and set aside.
Make the filling. Heat oil in a 10-inch cast iron skillet over medium heat until shimmering. Add onion, mushrooms, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Sauté for 4-6 minutes until onions are softened and dark bits form on bottom of skillet. Add tomato paste and garlic, then continue cooking and stirring about 2 minutes until bottom of skillet is dark brown. Add beer and deglaze, scraping up any browned bits. Stir in flour and cook for 1 minute. Add broth, Worcestershire, thyme, bay leaf, and frozen veggies; scrape up any additional browned bits and mix until broth and veggies are incorporated.
Reduce heat to medium-low, then add beef in 2-inch chunks to filling mixture, and bring to a simmer. Cover and cook until beef is cooked through, about 10 to 12 minutes, stirring and breaking up the chunks of beef halfway through. Create a cornstarch slurry by whisking cornstarch into 2 teaspoons water. Stir cornstarch slurry into filling and continue to simmer for 30 seconds. Remove thyme sprigs and bay leaf. Add salt and pepper to taste.
Add the topping and bake. Adjust oven rack 5 inches from your oven's broiler and set oven to broil. Place mashed potatoes in large Ziploc bag and cut off 1 corner to create a 1-inch opening. Pipe potato topping in even layer over filling. Smooth out the potato topping in an even layer with a spatula. If desired, use tines of fork to make ridges over surface. Place skillet on rimmed baking sheet and broil until potato topping is golden brown and filling is bubbly, 10 to 15 minutes. Let cool for 10 minutes before serving.
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