Heat the extra virgin olive oil in a small saucepan over medium-high heat then add the chopped mushrooms. Saute until the mushrooms release their liquid, the liquid cooks off, and the mushrooms become tender and golden brown, 5-7 minutes. Scrape the mixture into a bowl then set aside.
Lower the heat under the saucepan to medium then melt the butter inside. Sprinkle in the flour then whisk to combine and cook while whisking for 1 minute. Slowly add the chicken stock or broth while whisking to create a smooth sauce then add the milk and seasonings and whisk to combine. Turn the heat up slightly to bring the soup to a simmer while stirring constantly with a spatula then turn the heat back down to medium and continue to cook while stirring until the mixture is thick, 3-4 minutes. Add the mushroom mixture back into the pan then stir to combine. Scrape the soup into a very large mixing bowl to cool slightly, OR scoop into a glass storage container if making ahead of time. Soup can be made up 3 days ahead of time.
For the Casserole:
Add the butter to a 9x13” baking dish then place the baking dish inside the oven and start preheating it to 350 degrees. Once the butter has melted, remove the baking dish from the oven and set it aside.
To the mixing bowl with the Cream of Mushroom Soup, add the sour cream and pepper then whisk to combine. Add the green onions, diced ham, and shredded cheese then stir to combine. Add the thawed hash browns then fold until the mixture is thoroughly combined.
Scoop the hash brown mixture into the casserole dish with the melted butter then spread it into an even layer. Bake uncovered for 60-70 minutes or until the casserole is golden brown and bubbly all over, rotating the baking dish halfway through. Let the casserole cool for 20-30 minutes before scooping onto plates and serving.
Notes
I like Frick’s bone-in ham steak which I trim then dice into cubes. Your grocery store’s deli can also thick-slice ham into ham steaks, which you can then dice up. This is a great dish to make with leftover holiday ham.
To prep components ahead of time: up to 3 days ahead of time make the cream of mushroom soup, chop the green onions, and dice the ham.
To assemble casserole ahead of time: completely assemble the casserole up to the baking step up to 2 days ahead of time. Let the casserole dish sit out on the counter for 30 minutes before baking then bake covered in foil for the first 20 minutes.