In a bowl, combine the sliced chicken, canola oil, sesame oil, garlic, soy sauce, brown sugar, and lime juice. Toss to coat the chicken well and marinate for 20 minutes.
Heat a large skillet or non-stick pan over medium-high. Add the chicken and sear on all sides until cooked through and no longer pink, about 5 minutes. Remove from heat.
Fill a shallow bowl with warm water. Soak a single rice paper sheet for 5-10 seconds.
Remove and carefully place on a flat surface. Layer with chicken, spring mix, carrots, radish, and cilantro right in the center of the paper.
Fold both ends to the center and gently roll the sheet as tightly as you can without ripping. Continue with remaining sheets and filling. Then set aside for 1-2 minutes.
For the dressing, whisk all ingredients together.
Cut the rolls in half and serve with dipping sauce.