Preheat the oven to 350 degrees F. In a medium bowl, whisk together the eggs and milk. Add 1 cup of the shredded Cheddar cheese, and set aside.
In a 10-inch oven-proof skillet set over medium heat, cook the bacon until crisp. Drain, crumble, and set aside.
Remove all but a few teaspoons of the grease from the pan. You want just enough to lightly coat the bottom of the pan. (Alternatively, you may wipe the skillet clean and use olive oil.) Add the onion and cook over medium heat until softened. Add the thawed potatoes and cook, stirring occasionally, until golden on several sides. Sometimes, I turn the heat down to low and allow the potatoes to sit, undisturbed, in a single layer (checking occasionally) until crisp and golden brown. If you find your skillet seems dry at any point, drizzle with a little olive oil.
When the potatoes are cooked to your liking, scatter the cooked bacon over the top. Then pour in the egg mixture and, if necessary, use a fork to evenly distribute.
Immediately transfer the skillet to the oven and bake for about 10 minutes, or until the center is not quite set in the center. Sprinkle the remaining cheese on top, and continue baking for 3 to 4 minutes, or until the cheese is melted and the center is just cooked through. Remove from oven, and let sit 5 minutes before serving.