In a small bowl or jar, whisk or shake vinegar, mustard, and oil until combined and thickened; season with salt and pepper. (Dressing can be made ahead and refrigerated, covered, until ready to serve.)
In a large bowl, combine lettuce with dressing and 3/4 cup cheese; toss gently to coat. Divide among plates, and top with remaining 1/4 cup cheese. Serve immediately.
Use a sturdy vegetable peeler (a wide harp-shape one works best) to shave the Parmesan into long pieces.