Preheat oven according to tater tot bag instructions. Brown ground beef in a very large, oven-proof skillet (at least 10" - cast iron works great) seasoning with salt and pepper over medium-high heat. Drain then set aside.
Turn heat down to medium, melt butter in skillet, and then add mushrooms and shallots. Season with salt and pepper then saute until mushrooms start to soften, 3-5 minutes. Add garlic then saute for 1 more minute. Sprinkle in flour then whisk to combine and cook for 1 minute. Slowly stream in chicken broth and milk a splash at a time, whisking to avoid lumps. Add tamari/soy sauce, ketchup, worcestershire sauce, and smoked paprika, turn heat up slightly to bring mixture to a bubble, then turn heat back down to medium and simmer until just slightly thickened, 2-3 minutes.
Remove skillet from heat then stir in ground beef and arrange tater tots on top. Place skillet on top of a baking sheet (or place one on the rack below) then bake according to tater tot bag instructions. Let sit and thicken for 5 minutes before serving.
Most home cooks dump starches directly onto watery meat mixtures, ending in soggy potatoes. Understanding moisture barriers and starch thickening solves this issue entirely. Here is how chemistry dictates success in this pan.
Building the Roux Foundation
Fat coats the flour proteins when butter meets flour in a 1:1 ratio. Whisking chicken broth and milk gradually prevents clumping by hydrating starch granules evenly. Simmering the liquid for two to three minutes activates the thickening properties fully before baking begins.
Controlling Umami and Salt
Tamari, Worcestershire sauce, and ketchup introduce free glutamates that amplify beef flavor. Soy sauce and tamari can be substituted at an equal 1:1 ratio depending on dietary needs. Mushrooms release water during the initial three to five minute sauté, concentrating earthy flavors as moisture evaporates.
Securing the Potato Crust
Standard frozen potatoes require high oven heat to render internal moisture into steam. Placing the skillet on a baking sheet catches overflow and ensures uniform bottom heat distribution. Allowing the baked dish to rest for five minutes lets internal starches set for clean portioning.