In a saucepan, cover eggs with cold water and bring to a boil over high. Boil 1 minute, then remove from heat. Cover and let sit 10 minutes. Run eggs under cold water until cool enough to handle, then peel and halve lengthwise.
Meanwhile, season steak with salt and pepper. Heat a large skillet over medium-high. Place steak, fat side down, in skillet and cook until seared, browned, and medium-rare, about 7 minutes, flipping halfway through. Transfer to a cutting board and let rest 5 minutes before slicing against the grain.
Divide steak, lettuce, radicchio, tomatoes, onion, and eggs evenly among four plates. In a small bowl, whisk together oil and vinegar, and drizzle dressing over each salad. Season salads to taste with salt and pepper.
All it takes is some salt and pepper to make a delicious steak. It's okay to be generous; some of the seasoning will come off in the skillet.