Return the seared duck to the pot, turning it gently to coat it in the caramelized spice mixture. Pour in enough water to submerge at least half, or ideally two-thirds, of the duck. Add both soy sauces and fish sauce, stirring well to combine with the other ingredients.
Bring the mixture to a boil, then lower the heat to maintain a gentle simmer. Cover the pot with a tight-fitting lid and allow the duck to braise for 1½ to 2 hours, flipping the bird every 30 minutes to ensure even cooking and a deep, even color throughout.
In the final 30 minutes of cooking, gently nestle in tofu puffs and hard-boiled eggs if using, allowing them to absorb the savory richness of the braising liquid.