Preheat your charcoal or gas BBQ to direct heat at 240°C (470°F). Alternatively, cook in a pan, oven, or air fryer.
In a bowl, add the chicken, olive oil, and seasoning and mix to combine, coating the chicken evenly.
Add all of the herby mayonnaise ingredients to a bowl and mix to combine. Check and adjust the seasoning. Store in an airtight container or jar in the fridge until ready to serve.
Sear the chicken for 3–4 minutes on each side, or until golden and the internal temperature reaches 74°C (165°F). Add a slice of cheese in the last minute if using, so it melts. Remove and rest for 5 minutes.
Toast the buns or sandwich bread on the BBQ until lightly toasted. Spread one side with the herby mayonnaise and the other with a sauce or relish of choice. Layer with lettuce, tomato, red onion, the grilled chicken, and cheese. Close the sandwich and serve. Dig in.