Shred 2 ounces Parmesan. Shave remainder with vegetable peeler.
In food processor, combine shredded Parmesan, cream cheese, sun-dried tomatoes and 2 teaspoons oil from tomato jar. Puree until tomatoes are mostly chopped and good spreading consistency, 1 minute.
Transfer 1/2 cup to small bowl. Whisk in yogurt, milk, vinegar, sugar, salt and pepper for dressing.
Cut bread into 12 slices, 1/2 inch thick. Spread with remaining tomato spread, tablespoon per slice. Make 6 sandwiches with turkey, pepper strips, arugula and shaved Parmesan.
In bowl, mix cucumber, tomatoes and reserved sun-dried tomato-yogurt dressing. Serve with sandwiches. Makes 6 servings.