Preheat oven to 400°. Stir together butter, cream cheese, green onions, and garlic in a small bowl until combined; set aside.

Heat 1 tablespoon olive oil in a large cast-iron skillet over medium-high heat. Pat steaks dry with paper towels; cut steak into 1-inch pieces. Cook and stir pieces in cast-iron skillet for 4 minutes. Transfer steak to a bowl; set aside. Wipe skillet clean.

Heat additional 1 tablespoon olive oil in same skillet over medium heat. Add cooked potatoes and sprinkle with salt and ¼ teaspoon black pepper. Cook 8 to 10 minutes or until slightly golden. Add 1½ cups arugula. Continue cooking 5 to 7 minutes or until potatoes are golden brown and crispy. Add steak, half of the bacon, and the cream-cheese-butter. Toss to combine; remove from heat.

Make 4 (2-inch each) indentations in the potato mixture. Crack 1 egg into a custard cup, pour egg into center of indentation. Repeat with remaining 3 eggs. Sprinkle eggs with an additional ¼ teaspoon black pepper. Transfer skillet to oven; bake 4 to 5 minutes or until whites are firm and yolks are slightly thickened. Remove skillet from oven; top with remaining bacon and additional ½ cup fresh arugula.