Place the halved onion (cut-side down) and halved ginger (cut-side down) in a large, dry skillet or cast-iron pan. Heat over medium-high heat for 5 to 7 minutes, charring them until deeply browned and fragrant. Remove the charred aromatics and set aside. In the same pan, add the star anise, cinnamon stick, cloves, cardamom pods, and black peppercorns. Toast for 2 to 3 minutes over medium heat, stirring occasionally, until they become fragrant.
In a large stockpot (8-quart or larger), combine the whole chicken, charred onion, charred ginger, toasted spices, 12 cups of cold water, 2 tablespoons of fish sauce, 1 tablespoon of granulated sugar, and 1 teaspoon of fine sea salt. Bring the mixture to a rolling boil over high heat, then immediately reduce the heat to low, cover the pot, and simmer gently for 45 minutes to 1 hour, or until the chicken is cooked through and tender. During the first 15 minutes of simmering, use a spoon to skim off any foam or impurities that rise to the surface.
Carefully remove the cooked chicken from the stockpot and transfer it to a large cutting board or platter to cool slightly. Once the chicken is cool enough to handle, remove the skin and bones, then shred the meat into bite-sized pieces. Return the chicken bones (and skin, if desired for extra richness) to the stockpot and continue to simmer the broth, uncovered, for an additional 30 to 45 minutes to further develop the flavors.
Carefully strain the finished broth through a fine-mesh sieve into a clean pot or large bowl, discarding all the solids (ginger, onion, spices, and bones). Taste the hot broth and adjust the seasoning with more fish sauce or salt as needed. The broth should be rich, savory, and aromatic. Keep the strained broth hot over low heat while you prepare the remaining components.
While the broth simmers, prepare all your desired pho toppings. Roughly chop the fresh cilantro, thinly slice the green onions (scallions), wash and drain the fresh bean sprouts, cut the limes into wedges, and thinly slice the jalapeño. Arrange these prepared toppings in separate small bowls or on a platter for easy serving.
Following the package directions, cook the 1 pound of dried pho rice noodles in a separate large pot of boiling water until they are al dente, about 5 to 8 minutes. The noodles should be tender but still have a slight chew. Drain the noodles thoroughly in a colander and rinse briefly with warm water to prevent them from sticking together.
To assemble each bowl of pho, divide the cooked rice noodles evenly among individual large serving bowls. Top the noodles with a generous portion of the shredded chicken. Ladle the hot, flavorful broth over the chicken and noodles until everything is submerged and piping hot. Garnish each bowl generously with fresh cilantro, sliced green onions, bean sprouts, and sliced jalapeño. Serve immediately with lime wedges on the side for squeezing.