Fried Eggs with Greens and Mushrooms

Make the sage-chile butter: Melt butter in a saucepan over medium heat. Add sage and red-pepper flakes. Simmer until sage is crisp, about 3 minutes.

Make the eggs and greens: Heat a large, heavy skillet (preferably cast iron) over high heat. Swirl in oil. Cook mushrooms with 1/2 teaspoon salt until golden and tender, 4 to 5 minutes. Reduce heat to medium. Stir in garlic, then greens and water. Cook, stirring, until greens wilt. Add unsalted butter, and stir until melted.

Push greens to make 4 wells. Crack 1 egg into each. Season with salt. Cook for 4 minutes. Let stand until whites are set but yolks are still runny, about 4 minutes. Drizzle with sage-chile butter. Garnish with cheese.