• Gather all ingredients and have the frozen hash browns thawed before starting.

For the Cream of Mushroom Soup:

• Warm the olive oil in a small saucepan over medium-high heat. Add the chopped mushrooms and cook, stirring occasionally, until they release their liquid and turn golden-brown and tender, about 5–7 minutes. Transfer the mushrooms to a bowl and set aside.
• Reduce heat to medium and melt the butter in the same pan. Sprinkle in the flour and whisk continuously for about 1 minute to cook the flour. Gradually whisk in the chicken stock until smooth, then stir in the milk along with the onion and garlic powders and the 1/8 teaspoon pepper. Increase heat just enough to bring the mixture to a gentle simmer, stirring constantly, then lower the heat and keep stirring until the sauce thickens, about 3–4 minutes. Return the cooked mushrooms to the pan and mix to combine. Transfer the soup to a very large bowl to cool slightly, or store in a sealed container—this soup can be prepared up to 3 days ahead.

Assembly and Baking:

• Place the 3 tablespoons of butter in a 9×13-inch baking dish and put the dish in a cold oven. Preheat the oven to 350°F (175°C). Once the oven is preheated and the butter has melted, remove the dish and set it aside.
• To the bowl with the mushroom soup, whisk in the sour cream and 1/2 teaspoon black pepper until smooth. Stir in the sliced green onions, diced ham, and shredded cheddar until evenly distributed. Fold in the thawed hash browns until everything is thoroughly combined.
• Spoon the hash brown mixture into the buttered baking dish and smooth it into an even layer. Bake uncovered for 60–70 minutes, rotating the pan halfway through, until the top is golden and the casserole is bubbling. Allow the casserole to rest 20–30 minutes before serving so it firms up for easier slicing.