Step 1

Melt the butter in a large skillet over medium heat. Add the onion, cook until it softens and just begins to show signs of browning, about 5 minutes. Add the mushrooms and cook until browned and tender, and most of the liquid has evaporated, about 7 minutes. Stir in the salt and pepper.

Step 2

For each sandwich, top the bottom slice of toasted bread with mushrooms and onions. Place an egg over the mushrooms. Add a few leaves of arugula and add the top slice of bread. Serve warm.