01 - Combine shredded chicken, mayonnaise, Greek yogurt, Dijon mustard, celery, red onion, dill, lemon juice, salt, and pepper in a medium mixing bowl. Mix thoroughly until fully blended and creamy.
02 - Wash and dry cucumbers thoroughly. Using a mandoline or vegetable peeler, slice cucumbers lengthwise into long, thin ribbons. Aim for approximately 16 even slices.
03 - Place a cucumber ribbon flat on a clean work surface. Spread about 1 1/2 tablespoons of chicken salad along one end. Top with julienned carrots if using.
04 - Gently roll the cucumber ribbon around the filling, securing the chicken salad inside. Place seam side down on a serving platter.
05 - Repeat the rolling process with remaining cucumber ribbons and chicken salad mixture until all ingredients are used.
06 - Serve immediately for optimal crunch, or cover and refrigerate up to 2 hours before serving. Do not refrigerate longer or cucumbers will become soggy.