Heat the sesame oil in a pan over medium heat. Add the sliced red bell pepper and shredded carrots, stirring for about 3-4 minutes until slightly softened. Season with salt and pepper, then remove from heat.
In a large bowl, combine the grilled chicken slices with the sweet chili sauce. Mix until the chicken is fully coated in the sauce.
Take a tortilla and lay it flat on a clean surface. Place a generous portion of the sweet chili chicken in the center, then add the sautéed vegetables, cucumber, and fresh cilantro on top. If using, add avocado slices for creaminess.
Fold in the sides of the tortilla and then roll it up from the bottom to create a wrap. Repeat this process for the remaining tortillas.
For added warmth, you can briefly toast the wraps in a pan or a sandwich press until golden brown on all sides (optional).
Cut each wrap in half diagonally and serve immediately, paired with extra sweet chili sauce for dipping if desired.