Heat oil in a large pot over medium heat. Saute onions until translucent. To the onions add water, potatoes, salt and pepper. Bring to a boil; reduce heat to low and simmer for 20 minutes or until potatoes are tender but still firm.
Remove from heat and gently crack eggs into soup; be careful not to break eggs. Place on low heat until whites of eggs are cooked. Cool slightly before serving.