Remove silver skin from backstrap. Combine rosemary, pepper, salt and garlic, and spread out on a cutting board or work surface. Roll trimmed backstrap in rosemary mixture, and press firmly while rolling.

Heat 2 tablespoons of the oil in a large skillet. Carefully add backstrap, and cook on all sides for about 1 minute per side. The goal is for the rosemary mixture to adhere to the backstrap. Allow to cool completely before wrapping tightly in plastic wrap. Place in the freezer for at least 3 hours or until completely frozen.

Whisk together remaining olive oil, mustard, lemon juice, vinegar, capers, red onion and sugar.

Before serving, remove backstrap from freezer, and let rest at room temperature for 30 minutes to soften somewhat, but it should still be frozen. Using a sharp, thin-bladed knife, slice into rounds as thinly as possible without shredding. Think "paper thin." Arrange slices in a wide circle on plates. Lettuce mix will be placed in the center.

In a bowl, toss lettuce in a few tablespoons of the dressing, saving about the same amount of dressing to drizzle over backstrap. Mound lettuce in the center of plates. Drizzle remaining dress over meat. Top lettuce with Parmesan cheese.