Heat grill over medium-high heat (350- 400 degrees F) and oil the grill grates (to do this, dip a wadded paper towel in a little oil and, using tongs, wipe the oil evenly over the grate. Be careful not to use too much oil, because that's a surefire way to start a good flare-up—a little goes a long way here.)
Cook the chicken over the heat for 4 minutes per side, until the pieces turn golden and grill marks appear. The lid should be closed throughout the cooking process.
Flip the pieces once more and turn heat to medium-low, about 300°F, for 3-5 minutes, or until the chicken has cooked through and the internal temp is 165°F. Transfer the chicken to a cutting board and let rest for 5-8 minutes before slicing and serving.
To serve, layer 2 pieces of butter lettuce for the ‘wrap’. Fill with a few of the pickled carrots, then some sliced chicken, and finish with a few slices of cucumbers, some cilantro leaves and a sprinkle of toasted sesame seeds. Drizzle of the reserved sauce + squeeze of lime.
Enjoy!