Season both sides of the chicken breasts liberally with salt and pepper. In a skillet, heat one tablespoon of olive oil over medium-high heat. Carefully add the chicken breasts and cook for approximately 6-7 minutes on each side, or until they are thoroughly cooked through and reach an internal temperature of 165°F (75°C).
Reduce the heat to medium. Pour the teriyaki sauce over the cooked chicken, allowing it to simmer gently for 2-3 minutes. During this time, turn the chicken in the sauce to ensure an even coating.
Once the chicken has finished cooking, remove it from the skillet and place it on a cutting board. Allow it to rest for a few minutes to retain its juices before slicing it into thin, bite-sized strips.
Take a tortilla and lay it flat on a clean surface. Begin by placing a generous handful of shredded lettuce in the center. Next, layer on a few slices of the saucy teriyaki chicken, followed by the julienned carrots, cucumber, and vibrant slices of red bell pepper.
To wrap it up, fold the sides of the tortilla inward over the filling. Then, starting from the bottom, roll it tightly towards the top, ensuring the filling is securely encased within the tortilla.
Using a sharp knife, slice the wrap in half diagonally for a neat presentation. Optionally, sprinkle chopped green onions and sesame seeds on top for a decorative touch. Serve these delicious wraps with a small bowl of extra teriyaki sauce on the side for dipping.