Place the chicken in a large ziploc bag and use a pounder or the back of a large spoon. Pound them down to less than 1 inch thick (closer to ½ inch thick, ideally).
Using the ziploc bag you have (unless it is not usable), add the olive oil, 1 tbs of honey, 2.5 tsp of mint and the garlic, coating the chicken in the mixture. Marinate in the refrigerator for 5 hours or overnight.
Add the marinated chicken to a pan on medium heat. Cook covered for 5-6 minutes on each side or until cooked. When cooled, cut into slices.
Meanwhile, make the dressing. Cut one grapefruit in half and use a juicer to make ¼ cup of grapefruit juice. Add 3 tbsp of honey and 1½ tbs of mint to the grapefruit juice and mix.
Peel the other two grapefruit and segment off the membranes of the grapefruit.
Add the romaine lettuce, cucumber, chicken, grapefruit, and cashews. Drizzle the grapefruit honey mint dressing over the top.