Make the Fried Onions: Heat vegetable oil in a deep skillet or saucepan over medium heat until it reaches 350°F (175°C). Working in batches, add the thinly sliced onions and fry them for about 3-4 minutes, or until golden brown and crispy. Remove the onions and place them on a paper towel-lined plate to drain excess oil, then season with kosher salt. Set aside.
Make the Fried Onions: Heat vegetable oil in a deep skillet or saucepan over medium heat until it reaches 350°F (175°C). Working in batches, add the thinly sliced onions and fry them for about 3-4 minutes, or until golden brown and crispy. Remove the onions and place them on a paper towel-lined plate to drain excess oil, then season with kosher salt. Set aside. Whisk in the flour and cook for 1–2 minutes to remove the raw flavor. Gradually add the chicken broth and milk, whisking constantly until smooth. Stir in salt, black pepper, cayenne pepper, and dried mustard. Simmer for 2–3 minutes until thickened. Remove from heat.
Assemble the Casserole : Preheat your oven to 375°F (190°C). Grease a 9x13-inch baking dish. In a large mixing bowl, combine the thawed hash browns, melted butter, shredded cheddar cheese, sour cream, and the prepared sauce. Mix until evenly coated. Spread the mixture into the prepared baking dish.
Bake : Cover the dish with foil and bake in the preheated oven for 30 minutes. Remove the foil, sprinkle the top with the fried onions, and bake uncovered for an additional 15 minutes, or until bubbly and golden.
Serve : Allow the casserole to cool for 5 minutes before serving. Enjoy as a side dish for roasted meats, holiday meals, or potlucks.