Combine both rices in a medium bowl and cover with enough cold water to submerge. Soak for 30 minutes, then drain through a fine sieve and set aside.
Thinly slice 6 of the garlic cloves and place in a small pot with 1/4 cup of the vegetable oil. Place over medium-low heat and cook until garlic turns golden brown and crispy, 8-10 minutes. Remove the garlic chips with a slotted spoon and drain on paper towels. Meanwhile, chop the remaining 6 cloves and set aside.
Heat the remaining 3 tablespoons of vegetable oil in a 6-7 quart heavy bottom pot or Dutch oven over medium-high heat.
Season the chicken with the salt then brown in batches so as not to crowd the pan. Remove each batch to plate as it finishes. (Remember, we're browning the chicken here, not trying to cook it through.)
When the final chicken is out of the pan, add the onion, ginger, and remaining garlic to the pot and cook for 5 minutes. Stir in the fish sauce and white pepper and cook another minute.
Add the rinsed and drained rice to the pot and stir in the stock. Return the chicken to the pot, bring to a boil, then reduce the heat to medium-low. Cover partially with a lid, and cook for 30 minutes or until chicken is cooked through and the rice is tender and thickened into a loose porridge. Stir in the lime juice.
Ladle the Arroz Caldo into bowls, topping with the crispy garlic chips, sliced scallions, a squeeze of extra lime and a dash of extra fish sauce. Slice the soft boiled eggs in half and place on top of the dish with a drizzle of chili oil, if desired.