Preheat the oven to 400. Into a 9-inch baking dish, add two and a half cups of shredded hash browns, spread them out evenly.
Crack five eggs into a large bowl and add the half & half, use a wire whisk and whisk the mixture until the eggs and half & half are well-combined. Add chopped flat-leaf parsley, and diced red onion. Use the wire whisk to mix all of the ingredients.
Pour the quiche mixture over the shredded hash browns and scatter the shaved cheese mixture and sliced mushrooms over the quiche mixture.
Bake the quiche for forty minutes or until the quiche is set, about 35-40 minutes.
Remove from the oven and allow the quiche to cool for about fifteen minutes.
Serve.