To prepare the pudding, begin the day prior to serving. Place the chicken in a saucepan, ensuring it is fully submerged in water. Bring the water to a boil and cook the chicken until it is thoroughly done.
Once the chicken is cooked, transfer it from the pan to a bowl. Using your fingers, shred the meat into thin strips. For finer shreds, you can also use a fork to assist you. This process should be effortless if the chicken is cooked thoroughly.
Place the shredded chicken in a fine wire strainer and rinse it under cold water for a few minutes. Use your hand or a wooden spoon to press the chicken against the strainer while rinsing.
Afterwards, fill a bowl with cold water. Position the strainer over the bowl and immerse the shredded chicken in it for approximately 20 minutes. Drain the chicken in the strainer and repeat this procedure four to five times.
On the sixth iteration, position the strainer containing the shredded chicken in the bowl of cold water, and refrigerate the entire setup overnight. The following morning, drain the chicken, rinse it under running cold water a few more times, and thoroughly drain it by squeezing out any excess water. Set the shredded chicken aside for later use.
In a large saucepan, heat the milk and bring it to a boil for a few minutes. Add the shredded chicken to the milk and use a hand blender to blend it two or three times until it reaches a smooth consistency. Place the pan back on the heat and continue cooking for approximately 20 minutes, stirring constantly to prevent any sticking or burning.
In a separate bowl, combine the cornstarch, rice flour, and approximately two cups of water. Whisk the mixture until it becomes smooth. Take the milk off the heat, and while whisking continuously, gradually pour the starch mixture into the milk in a slow and steady stream. Keep whisking until the ingredients are well incorporated.
Once all the starch has been incorporated, place the pan back on the heat and continue stirring constantly as you bring it to scalding temperature. Cook the mixture for approximately five more minutes, stirring continuously, until it starts to thicken.
After that, add the sugar and vanilla to the mixture and cook for an additional 15 minutes. The pudding should become extremely thick, making it difficult to stir. Use the back of a wooden spoon to gently 'slap' the surface and keep it moving as it cooks.
Moisten the bottom and sides of a shallow glass tray, such as a rectangular oven casserole pan. Pour the pudding into the moistened tray and allow it to cool to room temperature. Once cooled, cover the tray with plastic wrap and refrigerate for approximately six hours.
To serve, you can either cut the pudding into slices or use a large spoon to scoop it out. Sprinkle a generous amount of cinnamon on each portion before serving.