Heat 2 tablespoons of olive oil in a nonstick skillet over medium heat. Season the chicken with salt and pepper, and cook for 5–7 minutes per side until golden brown and fully cooked, reaching an internal temperature of 165°F. Transfer to a cutting board and let rest for 5 minutes.

Slice the chicken thinly against the grain and combine it with 1/4 cup of teriyaki sauce in a bowl, ensuring even coating.

Shred 1 cup of carrots and 1 cup of red cabbage. Chop 1 cup of romaine lettuce. Warm tortillas in a skillet or microwave for about 20 seconds.

On each warm tortilla, spread a spoonful of mayonnaise or Greek yogurt if desired. Layer teriyaki chicken, carrots, cabbage, and lettuce. Fold in the sides of the tortilla and roll tightly from the bottom.

Cut each wrap in half diagonally for easier handling and serving. Serve immediately with extra teriyaki sauce for dipping.