In a small bowl, whisk together red wine vinegar, Dijon mustard, minced garlic, and a pinch of salt. Let sit 5 minutes so the garlic mellows slightly.

Slowly drizzle in the olive oil while whisking constantly until the dressing thickens and emulsifies. Taste and adjust salt if needed. Set aside.

Pat steak completely dry with paper towels. Season generously on both sides with salt and pepper. Let sit at room temperature for 15 minutes while you prep the salad.

Heat a cast iron skillet over medium-high heat until very hot, about 3 minutes. Add olive oil, then steak. Sear without moving for 4 minutes until a deep brown crust forms. Flip and cook 3-4 minutes more for medium-rare, or until an instant-read thermometer reads 130F in the thickest part.

Transfer steak to a cutting board and let rest 5 minutes - this keeps the juices from running out. Slice thinly against the grain.

In a large bowl, combine greens, tomatoes, and red onion. Drizzle with about half the vinaigrette and toss gently to coat.

Divide salad among plates. Arrange steak slices over the top, drizzle with remaining vinaigrette, and scatter Parmesan shavings. Serve immediately while the steak is warm.