Heat a dry, large skillet (I don't have a cast iron, but that would be preferred) over medium-high heat
Season steak with salt and better, then rub with vegetable oil entirely. Cook steak, turning once or twice to brown evenly, until medium-rare and slightly charred, 8-10 minutes. Transfer steak to a cutting board and leet rest at least 15 minutes. Reserve the skillet.
Chop the red onion and place slices in a bowl of cold water. Set aside.
Mix your vinaigrette: blend mustard and lemon juice with a fork in a small bowl. Then slowly pour in the olive oil, mixing as you pour to emulsify the liquid. Then gradually add the Parmesan. Add 1 Tbsp of cold water (if needed - taste first). Then continue to mix until smith and thick. You can do this all in a blender if preferred.
In the skillet that was reserved, turn the heat to medium. Drizzle cut length-wise slices of your bread with olive oil and place in the pan, cut side down. Cook until golden brown and crisp, about five minutes each.