Place the chicken in a large bowl and sprinkle with the garlic salt and white pepper. Toss to coat, then set aside. (If using turkey, you will season it with garlic salt and white pepper and add it later.)
In a large pot, heat the oil over medium-high until shimmering-hot. Add the onion, minced garlic, and ginger and cook, stirring occasionally, until softened and fragrant, about 5 minutes. Add the chicken and cook, stirring occasionally, until the skin begins to brown and the fat renders, about 5 minutes.
Stir in the rice so that it’s coated in chicken fat and cook for another 5 minutes, until the rice smells toasted and nutty. (At this point, if you’re using cooked turkey, season the shredded meat with garlic salt and white pepper to taste and add to the pan.) Pour in the broth.
Increase the heat and bring to a boil. Reduce to a low simmer and cook, stirring occasionally, until the chicken is nearly falling off the bone and the rice grains have broken down significantly, 45 minutes to 1 hour. Remove the chicken from the pot and let cool. (If you’re using turkey, just leave it in there.) Adjust the consistency with water as desired.
When the chicken is cool enough to handle, remove the meat from the bones and roughly chop, then stir it back into the arroz caldo. Season with the fish sauce, then divide among bowls. If desired, squeeze a calamansi or lime wedge over the top (serve extra wedges on the side) and garnish with fried garlic, scallions, X.O. sauce, and a soft-boiled egg.