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Step 1
Preheat the oven to 375 degrees Fahrenheit. Prepare the bottom and sides of a 9-by-13-inch baking dish with a bit of butter, oil, or cooking spray. Remove the hash browns from the freezer to allow them to thaw a bit. This will make it easier to combine them with the other ingredients.
Step 2
Heat a skillet over medium heat. Add the olive oil and swirl to coat the bottom of the pan. Add the onion and cook, stirring occasionally, until they begin to soften and become translucent, 3 to 4 minutes. Add the garlic and stir while cooking for 1 to 2 minutes. Remove the skillet from the heat.
Step 3
In a large bowl, combine the Velouté Sauce, the sauteed onions and garlic, sour cream, dried thyme, and approximately ⅔ of the shredded cheese. Stir with a spatula until well combined. Taste and season as needed with salt and pepper. Add the shredded hash brown potatoes and stir to combine.
Step 4
Transfer the mixture to the prepared baking pan, spreading to fill the dish evenly. Top with the remaining shredded cheese.
Step 5
In a medium bowl, combine the crushed cornflakes and melted butter. Toss gently to coat the cornflakes with the butter. Add the Parmesan cheese, dried thyme, and a bit of salt and pepper. Sprinkle evenly over the casserole dish.
Step 6
Transfer to the preheated oven and bake 30-40 minutes until golden brown and bubbling at the edges. If you prefer a deeply browned topping, you can place the dish under the broiler for a few minutes but watch closely as the topping will brown very quickly.
Step 7
Remove from the oven and allow the casserole to rest for 10 minutes before serving piping hot.