Marinate chicken pieces in a bowl along with lime juice, orange juice, rum, soy sauce, olive oil and apple cider vinegar. Refrigerate and marinate for 4 hours.
Preheat oven to 400 degrees F. Place a rack in the center of the oven and line two rimmed baking sheets with Reynolds Wrap(R) Non-Stick Foil.
Spread bread crumbs across one of the prepared baking sheets and bake until golden brown, about six minutes. Remove from the oven and set aside.
Whisk eggs in a medium bowl and set aside.
Toss together flour and cayenne pepper in a medium bowl and set aside.
Toss together the toasted bread crumbs along with sugar and spices on the rimmed baking sheet.
Remove the chicken pieces from the marinade and discard the marinade. Toss the chicken pieces lightly in the flour mixture.
Lightly coat the floured chicken pieces one at a time in the egg wash using a pair of tongs.
Transfer the coated chicken nuggets to the bread crumb and spice mixture and toss to coat, pressing the bread crumbs and spices into the nuggets. Place on the remaining prepared baking sheet in a single layer.
Bake chicken pieces for 13 to 15 minutes, flipping once during baking until cooked through.
Make the rice while the chicken bakes. Rinse basmati rice under cool water until the water runs clear. In a medium saucepan bring coconut milk and chicken broth to a simmer. Add the rice, lime juice and zest. Cover and cook until rice has absorbed all of the liquid, about 20 minutes. Remove from the heat and allow to rest for 5 minutes before fluffing. Top with black pepper and toasted coconut.