Preheat the oven to 425°F, setting rack to middle setting.
Making the Hash Brown Base
Rinse potatoes, then grate them with large holes of cheese grater. Either soak them in cold water, or rinse them under running water for a bit. Drain out any excess water and pat as dry as possible using paper towel or tea towel. I like to use a strainer to press out excess starch water.
Measure out 2 ½ cups shredded potatoes and transfer them to a medium-sized bowl. Toss with 1 tablespoon olive oil and salt and pepper to season lightly. Add 1 tablespoon olive oil to a 9" cast iron skillet (or oven safe skillet) and then add the potatoes. Press them down firm and flat. Bake the potatoes at 425°F for about 25-30 minutes, meanwhile make the egg mixture.
Make the Egg Mixture
In a large bowl, whisk together the eggs, milk, seasonings, parsley, and ¾ cup of the cheese. Add any additions of your choosing.
Once the hash brown base has baked, safely remove it from the oven. Decrease the oven temperature to 350°F. Drizzle olive oil around the edges of the hash browns, then sprinkle on the remaining ½ cup of cheese. Pour the egg mixture on top.
Place the skillet back in the oven, even if the temperature hasn't gone down to 350°F. Bake for 25-30 minutes or until the top is lightly browned.
Let cool for a few minutes before cutting into pie slices and serving. Serve with salsa or a salsa verde!