Place the soy sauce, olive oil, brown sugar, and ginger in a gallon-sized ziptop bag, seal tightly pressing out all of the air, and "squish" to combine. Add the chicken, firmly seal the bag again, and move the chicken around gently so that all sides are coated and it lays flat when the bag is on its side. Let marinade for 30 minutes or refrigerate overnight. (If refrigerating overnight, let the chicken stand at room temperature for 30 minutes prior to grilling.) Meanwhile, prepare the dressing and other ingredients.
Place the sliced red onions in a small bowl with water. Let sit while you prepare the rest of the salad (this mellows the red onions' bite, while maintaining their flavor; if you like the taste of raw red onion as is, you can feel free to skip this step).
Make the dressing: Puree the mango, lime juice, honey, cumin, coriander, and cayenne in your food processor until smooth. With the processor running, drizzle in the olive oil and blend to combine. Taste and adjust seasoning as desired. Use for salad, then store leftovers in an airtight container in the refrigerator for up to 1 week. Shake well before using.
Cook the chicken: Heat a grill pan or an outdoor grill over medium heat. Remove the chicken from the marinade, lightly shake off the excess, and grill for about 2 minutes per side, until cooked through (see ingredient notes for more information about length of cooking time). Remove to plate and let stand for 5 minutes. Cut into bite-sized pieces and set aside.
In a large bowl, combine the romaine, red bell pepper, black beans, and red onion. Add the chicken, drizzle with the mango lime dressing. Toss to coat. Scatter the oranges and cilantro over the top, then serve.
*If you cannot find thin-cut chicken breasts, you can use two regular chicken breasts by splitting them in half horizontally. Each of my thin-cut breasts weighed about 2.5 ounces and was less than a quarter inch thick. If your chicken breasts are thicker, you will need to grill them for longer.Store leftover mango dressing in the refrigerator for up to 1 week.