In a medium bowl, whisk together vinegar, mustard, mayonnaise, salt, and pepper. Slowly drizzle in the olive oil and whisk until it becomes a thickened emulsified dressing. Set aside.

Dry the surface of the steak with paper towels. Season both sides with salt and pepper.

Heat a large cast-iron skillet over high heat until hot. Add the oil. Once the oil is hot, add the steak and press it down into the pan. Cook until the surface is browned, 4 minutes. Flip the steak and cook until it reaches an internal temperature of 120 to 125°F (49 to 52ºC) on a meat thermometer for medium-rare, about 3 to 5 minutes.

Transfer the steak to a cutting board and rest for 10 minutes. Slice the steak against the grain into ¼-inch thick pieces. Cut smaller if desired.

In a large serving bowl mix together the arugula, romaine, and radicchio. Top salad with tomatoes, cucumber, radish, onion, steak, avocado, and feta cheese.

Serve steak salad with balsamic vinaigrette.