Cook bacon in a large nonstick skillet over medium heat 7 to 9 minutes until crisp. Transfer to a paper towel, leaving 2 tbsp fat in pan.
Spread hash browns in skillet; season with 1/4 tsp salt and pepper. Press into an even layer.
Cook undisturbed 6 to 8 minutes until bottom is deeply browned. Turn in sections; brown other side 4 minutes.
Whisk eggs, milk, and remaining 1/4 tsp salt until uniform in color.
Melt butter in a second skillet over medium-low heat. Add eggs; fold slowly 3 to 4 minutes until soft curds form with no liquid egg.
Divide potatoes among four bowls; top with eggs, cheddar, bacon, tomato, and scallions.