Melt butter in a small saucepan over low heat. Sprinkle in the flour and whisk. Cook for about 30 seconds.
Stir in chicken stock and whisk to remove any clumps. Simmer until it starts to thicken, then stir in milk and all of the seasonings. It should be thickening nicely by now. Taste and adjust seasonings as needed then set aside. I needed to add a bit more pepper.
Heat olive oil in a large skillet over medium-high heat until just smoking.
Brown the sliced chicken sausage slices a bit on both sides for just a couple of minutes (since sausage is already pre-cooked). Set aside. This step will bring out the best flavor of the sausage.
Pour hash browns, chicken sausage, onion and cheese together in a lightly greased crock pot/slow cooker. Pour the condensed cream of chicken soup you just made over all of it and stir until incorporated.
Cover and cook on high for 3 hours or until potatoes are soft and sausages are hot (may be done sooner). Serve warm. If using for a brunch or pot luck, leave crock pot on warm setting as long as you need. Enjoy!