Heat oven to 375°F. Squeeze thawed potatoes in a clean towel until no longer dripping; separate compacted shreds.
Heat 1 tablespoon oil in a 12-inch oven-safe skillet over medium-high. Spread half potatoes loosely; brown underside 6 to 7 minutes. Turn in sections; cook 3 minutes. Transfer to large bowl; repeat with remaining oil and potatoes.
Reduce to medium; melt butter in same skillet. Cook onion 5 minutes until soft; remove from heat.
Whisk sour cream, milk, salt, pepper, and 6 ounces cheddar. Fold with cooked onion into potatoes. Return to skillet; spread evenly without packing.
Top with remaining cheddar; bake 20 to 25 minutes until center bubbles and patches turn golden. Rest 10 minutes before scooping.