Soak the rice. Transfer both the uncooked glutinous sticky rice and the medium-grain rice (Calrose or Jasmine rice) to a large bowl and cover with cold water. Set aside to soak.
Prepare chicken stock. Transfer the chicken (whole or chopped into smaller pieces) to a large stockpot and fill with at least 12-15 cups of water, or enough water that the chicken is covered. Bring to a boil over medium-high heat. Once boiling, reduce heat to a simmer. Allow the chicken to cook for approximately 45-60 minutes, or until the thickest part of the chicken registers 160 degrees F with a digital meat thermometer (as the chicken simmers, use a large slotted spoon to skim any frothy scum from the surface). Once the chicken is cooked through, remove to a clean plate to cool. Leave the homemade chicken stock behind in the pot.
Fry the sliced garlic. After the chicken has been simmering for approximately 30-45 minutes, thinly slice 5-6 garlic cloves. Heat the vegetable oil (canola oil, peanut oil, or sunflower oil are all great options) in a large saucepan or Dutch oven over medium-high heat. Add the garlic and toast until golden brown. Use a slotted spoon to remove and transfer to a plate lined with paper towels to drain.
Sauté the aromatics. Return your saucepan or Dutch oven (with any leftover oil) to medium heat. Add the diced onions and cook, stirring occasionally, for 5-6 minutes, or until softened and translucent. Add the minced garlic and julienned ginger. Mix well to combine. Cook, stirring continuously, for 1-2 minutes, or until fragrant. Season with a pinch of salt.
Toast the rice and add the fish sauce. Rinse and drain the rice really well. Transfer the uncooked rice to the pot with the onions, garlic, and ginger. Toast the rice for 2-3 minutes, stirring often to prevent the rice from sticking or burning. Stir in the fish sauce, mixing well to combine.
Cook. Add approximately 16 cups of your homemade chicken broth to the pot (yes, you will need a large pot). Mix thoroughly to combine and bring to a boil. Once boiling, reduce heat to medium-low, and half-way cover your pot with a lid. Simmer, stirring occasionally, for 30-40 minutes, or until the rice has thickened and taken on a creamy consistency. Thin with additional chicken broth or water, as needed.
Shred the chicken. As the porridge cooks, shred your chicken, saving as much or as little skin as you'd like, and discarding all bones. You may add the chicken directly to the cooking rice, or divide among bowls.
Garnish and serve. Ladle generous spoonfuls of hot Arroz Caldo among bowls and garnish with hard-boiled eggs, chopped green onions, fried garlic, ground black pepper, and shredded chicken.