Tear frisee and red-leaf lettuce into bite-size pieces; combine with spinach in a large bowl. Set aside.
In a blender, combine cranberries, vinegar, lime juice, sugar, salt, and oil; puree until mixture is smooth.
Sprinkle dried cranberries over salad greens in bowl; toss to combine. Divide salad among serving plates. Using a vegetable peeler to shave thin slices, divide cheese among individual salads. Serve with cranberry vinaigrette on the side.