Marinate the Chicken: In a medium bowl, whisk together the white wine, reduced-sodium soy sauce (marinade portion), 1 ½ tablespoons toasted sesame oil, lemon juice, Dijon mustard, red pepper flakes, and minced garlic. Place the chicken breasts in a large resealable bag or glass dish and pour the marinade over them, ensuring all pieces are well-coated. Seal or cover and refrigerate for at least 4 hours (overnight is ideal).
Cook the Chicken: Preheat your grill to medium-high heat (375-450°F / 190-230°C) or preheat your oven broiler with the rack positioned 6 inches from the heat source. Remove chicken from the marinade, allowing excess liquid to drip off (discard the used marinade). Grill or broil for 5-7 minutes per side until the internal temperature reaches 165°F (74°C).
Rest and Slice: Transfer the cooked chicken to a clean cutting board and tent loosely with foil. Let rest for 10 minutes to lock in juices. Slice against the grain into bite-sized strips. Place these strips into a large mixing bowl.
Prepare the Dressing: While the chicken rests, combine the 2 whole garlic cloves, sherry vinegar, reduced-sodium soy sauce (dressing portion), and 1 ½ tablespoons toasted sesame oil in a food processor or blender. Pulse until the garlic is finely minced. With the machine running on low, slowly stream in the extra virgin olive oil until the dressing is smooth and emulsified.
Assemble: Pour the dressing over the warm chicken strips in the large bowl. Add the red onion, snap peas, cucumber, dried cranberries, and black pepper. Toss gently to ensure everything is well-coated.
Serve: Add the fresh arugula last, tossing very lightly to combine without wilting the greens excessively. Sprinkle with almonds or sesame seeds if using. Serve immediately.