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 all ingredients are fully incorporated and the mixture reaches a spreadable consistency.
02 - Wash and pat dry the English cucumbers. Using a mandoline slicer or vegetable peeler, slice each cucumber lengthwise into long, thin ribbons. Aim for approximately 16 even, pliable slices that can be easily rolled without breaking.
03 - Lay a cucumber ribbon flat on a clean work surface. Spread approximately 1 1/2 tablespoons of the chicken salad mixture evenly along one short end. Add a few julienne carrots on top if using for added crunch and color.
04 - Starting from the filled end, gently roll the cucumber ribbon around the chicken salad filling to create a tight cylinder. Place each roll seam-side down on a serving platter to prevent unrolling.
05 - Repeat the rolling process with remaining cucumber ribbons and chicken salad until all filling is used. Ensure rolls are uniform in size for consistent presentation.
06 - Serve immediately for optimal crunch, or cover and refrigerate for up to 2 hours before serving. If refrigerating, bring to room temperature for 10 minutes before serving to enhance flavor.