Step 1

Combine the onions and olive oil in a large skillet and cook gently over moderate heat (“low and slow,” as Aggie says) until the onions are softened and shiny but have not taken on any color, about 10 minutes. Add the water and bring to a boil, then reduce the heat to moderately low and simmer until the onions are soft, silky, and can “melt in your mouth,” about 10 minutes.

Step 2

Meanwhile, beat the eggs with 1 teaspoon kosher salt. Turn off the heat under the onions and slowly drizzle in the eggs, stirring all the while with a fork — the eggs will cook into soft threads.

Step 3

Season the mixture with salt and pepper to taste. To serve, set out 4 shallow soup bowls and lay a slice of stale bread in each. Ladle the fried water over the bread and serve at once.