In a medium bowl, whisk together the broth, coconut milk, soy sauce, shallot, garlic, fish sauce, brown sugar, lime zest, and ginger. Add the chicken pieces, turning to coat. Cover with plastic wrap and marinade in the fridge for 1 hour.
Remove chicken from marinade and discard the marinade.
Coat a grill pan, preferably cast-iron, with nonstick spray and set it over medium-high heat. While the pan is heating, thread the chicken onto skewers. Place skewers in the hot pan and sear until cooked through and the chicken has grill marks, about 3 minutes per side.
For the sauce:
Place all ingredients in a blender and blend until smooth. Add more chicken broth or coconut milk if thinner consistency is desired. Sauce will keep in the fridge for up to 3 days.