Preheat your oven to 350°F. This will be the starting point for roasting your vegetables and bones, which is crucial for developing flavor.
Place the onion, ginger, and chicken bones in a roasting pan. Roast them for one hour, making sure to move them around after about thirty minutes to ensure even cooking. This step enhances the flavors significantly.
Once roasted, remove them from the oven and let them cool. Peel the onion and cut it in half, then slice the ginger into thin pieces without peeling it.
In a large stock pot, combine the roasted onion, ginger, bones, water, salt, and brown sugar.
Bring the mixture to a boil, then reduce the heat to a simmer. Let it simmer for three hours, adding an extra quart of water if necessary. The liquid should remain about one inch above the bones.
Using a large slotted spoon, carefully remove the bones and larger vegetable chunks from the broth. Strain the stock through a fine-mesh sieve into a heatproof bowl or pot, and let it cool for at least one hour.
While the broth is cooling, prepare a medium saucepan with enough vegetable oil to come up about one-third of the way up the pan. Heat the oil until it reaches 340°F on a deep-fry thermometer.
Fry the shallots in the hot oil for about four to six minutes, stirring constantly until they are light golden brown. Be careful not to burn them! After frying, transfer to a paper towel-lined plate to drain.
In a separate large pot, bring water to a boil over high heat. Add the chicken, scallions, ginger, and salt to this pot and boil for fifteen minutes. Turn off the heat, cover, and let it sit for twenty-five minutes.
Prepare an ice-water bath in a large bowl just before the chicken is done. When finished, use tongs to remove the chicken and immerse it in the ice-water bath to stop the cooking process.
Let the chicken chill for around twenty minutes until it’s cool enough to handle. Once cooled, remove the meat from the bones and shred it. You should end up with about four cups of shredded meat.
Return the strained stock to the stove and bring it to a simmer over medium-high heat. Taste the broth and adjust the seasoning by adding more salt or fish sauce, if needed.
Prepare the rice noodles according to package directions, then distribute them evenly among soup bowls.
Set up a platter with your garnishes: basil, bean sprouts, lime wedges, jalapeños, and fried shallots.
Top each bowl of noodles with about three-quarters of a cup of shredded chicken and divide the scallions and cilantro evenly among the bowls.
Finally, ladle the hot stock over each bowl, sprinkle with fried shallots, and serve immediately with the garnishes on the side!