Put a 10-inch skillet with a lid over medium heat. If you do not have a lid, set a large plate or sheet pan nearby to cover the skillet later.

Add the olive oil to the skillet and heat it for about 30 seconds, until it looks loose and shiny.

Add the frozen hash browns to the skillet. Spread them into an even layer and sprinkle with about 1/2 teaspoon of the salt and a few grinds of black pepper.

Cook the hash browns without stirring for 5 minutes, until the bottom is deep golden brown in spots.

Add the chopped onion to the skillet. Stir the onion into the hash browns, then spread the mixture back into an even layer.

Cook for 4 to 5 minutes more over medium heat, stirring once halfway through, until the onion is softened and the potatoes are golden in several spots.

Add the frozen peas to the skillet. Stir them through the potatoes and cook for 2 minutes, until the peas are hot and no longer icy.

Season the skillet with the remaining 1/2 teaspoon salt and more black pepper. Taste a small bite of potato and add a little more salt if needed.

Lower the heat to medium-low. Use a spatula to press the hash brown mixture into a fairly flat layer across the bottom of the skillet.

Sprinkle the shredded cheddar over the potatoes, leaving a little space where the eggs will sit. Let it melt for about 30 seconds.

Use the back of a spoon to make 4 shallow wells in the potato mixture.

Crack 1 egg at a time into a small cup, then slide each egg into a well in the skillet. This makes it easier to place the eggs neatly and catch any shell pieces.