In a small saucepan set over medium-high heat, add the sesame and peanut oils. Once the oils are hot, about 30 seconds, add the onions to the pan and cook, stirring often until the onions are soft and slightly translucent, about 3 to 4 minutes. Add the garlic, ginger, cinnamon and star anise to the pan and cook for 30 seconds. Deglaze the pan with the lime juice and soy sauce. Once the juice has reduced by half, add plum sauce, crushed red pepper flakes, water and mustard. Reduce the heat to a gentle simmer and cook the sauce for 5 minutes. Remove the sauce from the heat and discard the cinnamon stick and star anise. Reserve the sauce until ready to use.
Combine the kosher salt and Chinese five-spice in a small bowl and stir to mix well. Season the chicken with the salt mixture and set aside for 20 minutes.
Cook the chicken on a medium hot grill for 2 minutes then turn 45 degrees and cook for an additional 2 minutes. Turn the chicken over and cook for 2 minutes before rotating it 45 degrees to cook for a final 2 minutes. Remove the chicken from the grill and place on a sheet pan that has been lined with aluminum foil. Squeeze lime juice over chicken, brush the chicken with the barbecue sauce, and place the sheet pan in the oven. Cook the chicken for 5 minutes, remove from the oven and serve while warm.