Prep the side salad by combining the chopped lettuce, tomato, and carrot. Set aside for later.
Mix the black pepper, salt, paprika and onion powder in a small bowl to create a steak rub. Thoroughly coat the steak with the spice rub.
Heat 1 teaspoon of oil in a heavy cast-iron skillet over medium heat. When the pan is hot, add the steak, and cook for 3 minutes on each side, or until cooked to desired done-ness. Remove steak from the pan and place it onto a plate.
Add another teaspoon of oil to the hot pan and fry the two eggs. Top the steak with the eggs and serve with the side salad. Add a squeeze of fresh lemon juice to the side salad.