Heat the oven to 375°F. Squeeze thawed potatoes in a clean towel until they stop dripping, separating compacted shreds afterward.
Heat 1 tablespoon oil in a 12-inch oven-safe skillet over medium-high heat. Spread half the potatoes loosely in the pan, cook for 6 to 7 minutes until the underside browns and turn in sections for 3 minutes; transfer to a large bowl and repeat with remaining oil and potatoes.
Reduce the heat to medium, melt butter in the same skillet and cook onion for 5 minutes until soft. Remove from the heat.
Whisk sour cream, milk, salt, pepper and 6 ounces cheddar together. Fold this mixture and the cooked onion into the potatoes, then return everything to the skillet and spread evenly without packing it down.
Scatter remaining cheddar over the top and bake for 20 to 25 minutes until bubbling in the center and golden in patches. Rest for 10 minutes before scooping.