Combine ¾ cup sun-dried tomatoes, ½ cup mayonnaise, ½ cup yogurt, ¼ cup Parmesan, 2 tablespoons shallot, 2 teaspoons vinegar, 1 teaspoon mustard, ¼ teaspoon crushed red pepper, ¼ teaspoon garlic powder and ¼ teaspoon salt in a medium bowl; stir well. Fold in 3 cups chicken until evenly coated.
Top each of 4 bread slices with 1 cup chicken salad and ½ cup arugula. Top with the remaining 4 slices. Cut the sandwiches in half diagonally.
