Combine the ponzu, lime juice, and garlic. Pour over the chicken and marinate for at least 4 hours, but preferably overnight.
Before cooking, drain the chicken, pat dry with towels, and discard garlic pieces. Brush both sides of the chicken lightly with canola oil and season with salt and pepper.
Grill over direct medium heat for 2 ½ to 3 minutes per side, or until well-marked and cooked through. Grill the buns, cut side down, for about 30 seconds. (Alternately, the chicken and buns can be broiled, cooked on a flat-top griddle, or in a sauté or grill pan.)
Place the lettuce and tomato slices on the bottom of the bun and top with a chicken filet. Spoon 1 teaspoon of the wasabi sauce over chicken, or more, to taste. Serve with pickled carrots and garnish with micro greens, if desired.