Santa Fe Breakfast Potatoes And Eggs

In a medium saucepan, cover the potatoes with cold water. Set over medium heat, bring to a boil, and cook until just tender, about 30 minutes. Drain and cool.

Peel the potatoes if you wish and cut them into 1/2-inch cubes (The potatoes can be prepared up to 1 day ahead; cover and refrigerate).

In a large heavy skillet over medium heat, melt the butter. Add the onions, cover, and cook for 5 minutes. Uncover and cook, stirring occasionally, until lightly browned, about 20 minutes.

Scatter the cheese over the potatoes, cover the skillet, and remove from the heat. Let stand until the cheese is melted, about 1 minute.

Meanwhile, set a large skillet of water over medium heat and bring it to a simmer. Stir in the vinegar. Regulate the heat to avoid an active boil, and use a slotted spoon to gently shape the eggs into tidy ovals. Cook until done to your liking, about three minutes for fairly soft eggs.

Spoon the potatoes into serving bowls. With a slotted spoon, lift the eggs one at a time from the water, drain briefly, and then set two eggs atop each bowl of potatoes. Spoon the chili sauce over each portion and serve immediately.