Whisk oil, vinegar, garlic, and crushed red pepper in large bowl. Add radicchio and romaine and toss to coat. Marinate 20 minutes.

Prepare barbecue (medium heat). Drain marinade into small bowl. Place radicchio and romaine on grill; sprinkle with kosher salt and fresh cracked pepper.

Grill radicchio and romaine until edges are crisp and slightly charred, turning occasionally, about 6 minutes. Transfer to serving platter. Drizzle with reserved marinade and sprinkle with cheese shavings.