Add the boneless chicken and toss together to coat properly. Cover and refrigerate for at least 2 hours or leave overnight.
Remove the chicken from the pan and then transfer it to a cutting board. Slice the chicken into thin pieces. Transfer the chicken back to the grill pan, and cook for 1-2 minutes enough to heat and crisp up the chicken. This along with the brown sugar caramelises the chicken from the outside, and gives it the shawarma like effect at home
Put the finely chopped cucumber in a colander and sprinkle salt on top. Let this sit for an hour with a plate below it in the fridge so that the water from the cucumber is is reduced.
Add the cucumber along with crushed & chopped garlic to the yoghurt. Add lemon juice and mix it all up. Taste and adjust as required.
There are two ways that this chicken shawarma can be rolled. One method is by folding the edges from top and bottom, and then rolling it up spring roll style, after which the shawarma roll can be cut into half. The other method is folding from one end, and then rolling it up so it becomes a chicken shawarma wrap that is open from one end.
Serve with more Tzatziki sauce, chili sauce, hummus or baba ganoush on the side.