In a saucepan, combine the sauce ingredients. Bring to a simmer over medium-low heat, then reduce the heat to low to gently simmer as you prepare the rest of the meal; stir occasionally.
Preheat your oven to 250°F. In a wok or skillet, warm the coconut oil over medium heat. Combine the tapioca starch, salt, and pepper, then toss the chicken pieces with the starch mixture. With your fingers, dip a starchy chicken piece in the beaten eggs, shake off the excess egg, and then add to the oil. Repeat until you have filled your skillet, being careful not to overcrowd the chicken pieces. Fry the chicken until cooked through, flipping every 2 minutes, about 6 to 8 minutes per batch. As you finish each batch, place the cooked pieces on a plate lined with paper towels; put them in the oven to stay warm. You should be able to cook the chicken pieces in 3 or 4 batches, depending on the size of your skillet.
Once the chicken is cooked through, finish the sauce. Taste the sauce and add more salt or pepper if needed. If the sauce is too dark and strong tasting, add a little chicken broth to thin it out. At this point, the sauce should be about as thick as tomato soup and should have a sharp but not overwhelming flavor.
In a small bowl, stir together the arrowroot starch and cold water to create a slurry. Raise the sauce temperature to medium; once bubbling, add half of the slurry and stir until thickened, adding more slurry if needed. Remove from the heat.
Toss the chicken pieces with the sauce, then garnish with sesame seeds and green onions. Serve over Basic Steamed Rice or Cauliflower Rice. (See below for recipes)