In a medium-large bowl, mix together grated garlic, soy sauce, hoisin sauce, peanut butter, sweet chili sauce, sesame oil, lemon juice and grated ginger. Add chickens to the bowl and marinate in a refrigerator for 1 hour.
In the meantime, make salad. In a bowl, mix together julienne carrots and salt. Let sit for about 10 minutes or until carrots are tender. After 10 minutes when the carrots are tender, with hands, squeeze the carrots to drain completely. Put into another bowl and add cucumbers, sugar and rice wine vinegar. Mix until well coated. Set aside.
After 1 hour, take the chickens out of the refrigerator. Heat skillet or fry pan and cook chickens over medium heat until cooked through. Put the sauce remaining in the bowl into the skillet/fry pan and toss to coat. Turn off the heat and let cool.
Brush butter on the bottom of each bun and toast the buns (both bottom and top of the buns) lightly.
Build sandwiches. On the bottom of each bun, place lettuce leaves. Squeeze the salad to drain and put on the lettuce, then put the chickens. Put the top of the bun to close sandwich.