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 is creamy and uniform.
02 - Wash and dry cucumbers thoroughly. Using a mandoline slicer or vegetable peeler, slice cucumbers lengthwise into long, thin ribbons. Aim for approximately 16 even, pliable slices that will roll easily without tearing.
03 - Lay a cucumber ribbon flat on a clean work surface. Spread approximately 1 1/2 tablespoons of chicken salad mixture evenly along one short end. Add a few julienned carrots on top if using. Gently roll the cucumber starting from the filled end, tucking in the filling as you roll. Place seam side down on a serving platter.
04 - Repeat the rolling process with remaining cucumber ribbons and chicken salad until all components are used. Serve immediately for optimal crispness, or cover and refrigerate for up to 2 hours before serving. If refrigerating, bring to room temperature for 10 minutes prior to serving.