Cut off and discard the green tops of the onions and thinly slice the white portions. Soak the onions in water to cover for 1 hour.
Drain the onions well. Put them in a skillet with the oil and cook slowly, without browning, until translucent. Add the arugula, season with salt and pepper, and let wilt for a few minutes, stirring.
Break the eggs into a bowl, season lightly with s