• 2 tablespoons extra-virgin olive oil   
• 1 garlic clove, peeled and crushed   
• ¾ cup mixed mushrooms, halved or quartered     
• 2 tablespoons finely chopped flat-leaf parsley   
• Salt
• Freshly ground black pepper
• 1 cup freshly grated Parmigiano-Reggiano   
• 4 large eggs   
• 3 tablespoons heavy cream

In a large skillet, heat oil. Add garlic and cook over low heat until fragrant, about 3 minutes. Add mushrooms, 1 tablespoon of the parsley, and a pinch of salt and pepper. Cook, stirring, until mushrooms are tender, about 5 minutes. Remove from heat and adjust seasoning.

Heat a second large nonstick skillet over medium heat. Add 4 tablespoons of the Parmigiano-Reggiano in a 4½-inch round and cook until golden and bubbling, 3 to 4 minutes, turning once. Using a thin spatula, transfer the parmesan crisp to a plate to cool. Wipe out skillet and repeat to make 3 more crisps.

Bring a large saucepan of water to boil. In a medium metal bowl, lightly beat eggs with heavy cream and pinch salt. Place bowl about ¾ inch into boiling water. Cook eggs, whisking, until loosely set.

Divide eggs among 4 bowls and top with mushrooms, parmesan crisps and remaining parsley. Serve at once.