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In a small bowl, combine the oil, scallions, parsley, vinegar, pepper, and garlic. Season with salt and pepper. Cover and refrigerate until ready to serve.
Heat a large cast iron skillet over medium-high and pour in 1 tablespoon of the oil. Add the steak and cook until golden on both sides and center reaches 125°F for medium-rare, about 5 minutes per side.
Transfer steak to a cutting board and remove skillet from heat.
Drain excess fat from skillet and wipe clean. Place skillet over medium heat and pour in the remaining 2 tablespoons of oil. Crack the eggs into the skillet, season with salt and pepper, and cook until whites are just set, and yolks are still runny, about 5 minutes; transfer to plates.
Thinly slice the steak and arrange on plates with eggs.
Dollop with scallion relish and hot sauce and serve with toast or roasted potatoes.
¼ cup extra-virgin olive oil
3 large scallions, thinly sliced (about ½ cup)
⅓ cup packed fresh parsley leaves, finely chopped
2 tablespoons red wine vinegar
1 teaspoon aleppo pepper, or large pinch red pepper flakes
1 small garlic clove, finely grated
Kosher salt and freshly ground black pepper
3 tablespoons extra-virgin olive oil
1 ½ pounds Flank steak, cut into 4 equal size pieces
4 large eggs
Toast or roasted potatoes, for serving
Hot sauce, for serving