Prep Time: 60 minutes
Place the potatoes in a large pot in a single layer and cover with an inch of water. Add a pinch of salt and bring to a boil. Cook until easily pierced with a fork, about 15-20 minutes. Drain and dry completely. Set aside.
While the potatoes are boiling, preheat the oven to 425 degrees. Oil a sheet tray with 1 Tbsp. olive oil. When the potatoes are cooked and dried, place them on the sheet tray. Press down on each potato gently with a spatula to smash. In a small bowl, combine 3 Tbsp. olive oil with the herbs and pour evenly over the potatoes. Season with a pinch of salt and pepper and place in the oven until crispy, about 30 minutes.
When the potatoes are 15 minutes from being done, heat 1 Tbsp. oil in a large heavy skillet, preferably cast iron, over a medium-high flame. Season the steak with a pinch of salt on each side and add to the hot pan. Cook for about 4 minutes on each side for medium rare, 5 minutes for medium. Remove to a plate to rest for 5 minutes. In the same pan, cook the mushrooms in 1 Tbsp. olive oil, stirring occasionally. In a separate skillet over medium heat, add 1/2 Tbsp. oil until hot. Add the eggs and fry to your desired likeness.Slice the steak across the grain and divide evenly among two plates. Garnish with the mushrooms. Finish each plate with the potatoes and fried eggs.