Set a 12-inch skillet with a lid over medium heat. Add the olive oil and let it warm for about 30 seconds.

Put the potatoes into the skillet. Sprinkle them with 1/2 teaspoon of the salt and stir so the pieces are coated with oil.

Pour 1/4 cup water into the skillet. Cover with the lid and cook for 5 minutes so the potatoes can soften.

Remove the lid. Cook the potatoes uncovered for 6 to 8 minutes, stirring every 2 minutes, until most of the water is gone and the potatoes are starting to brown on the edges.

Add the sliced onion to the skillet. Stir the onion into the potatoes.

Cook for 4 to 5 minutes, stirring now and then, until the onion is soft and the potatoes are tender when pierced with a knife.

Add the capers to the skillet. Cook for 30 seconds so they warm through and mix into the potatoes.

Scatter half of the smoked salmon over the potato mixture in the skillet. Leave the rest for the finish.

Dot the cream cheese pieces around the skillet, placing them between the potatoes instead of in one pile.

Use the back of a spoon to make 6 shallow spaces in the potato mixture. Keep the skillet over low heat.

Crack 1 egg into each space in the skillet. Sprinkle the eggs with the remaining 1/4 teaspoon salt and about half of the black pepper.

Cover the skillet and cook on low for 4 to 6 minutes. The eggs are ready when the whites look fully opaque and set, and the yolks are still soft or cooked to your liking.