1. Preheat oven to 400F. Lightly grease a 9×13 inch baking dish.
2. Shred the potatoes using cheese-shredding side of the box grater. Transfer to a large bowl. Fill with cold water. Swish them around. Drain them using a big colander. Return the potatoes to the bowl. Fill with more cold water and set aside.
3. Heat the butter in a large nonstick skillet over medium heat. Add the onion and cook until softened, 3-4 minutes. 
4. Add the flour and stir to distribute. Cook while stirring for 1 minute.
5. Stir in the milk, 1 teaspoon of the salt, and the pepper. Continue to stir and cook over medium heat until the sauce is bubbling and thickened, 2-3 minutes. Remove from heat.
6. Drain the potatoes in the colander. Press on them a bit to remove excess water. 
7. Transfer potatoes to skillet with the sauce. Sprinkle with the remaining teaspoon of salt. Stir to moisten all potato shreds evenly. 
8. Return skillet to the heat. Stir and cook until steaming and bubbling. Stir in 1 cup of the cheese.
9. Transfer the potato mixture to the prepared baking dish. Smooth out the top, but don’t pack it in, just scoop it and smooth it.
10. Cover with foil. Bake until it’s bubbling in the middle, the edges are brown, and the potatoes in the middle are tender (taste some to make sure), about 40 minutes. 
11. Remove from oven. Remove foil. Sprinkle potatoes with remaining 1 and 1/2 cups of cheese. Bake until cheese is melted and starting to brown, about 15 minutes.
12. Sprinkle with green onions and serve.

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