Peel and slice ginger into 5 or 6 coins. Chop 3 green onions into segments, 2 inches each. Bruise ginger slices, green onion segments, and garlic clove by hitting them with flat side of a knife. Set aside.

In large saucepan over medium heat, place coriander seeds, star anise, clove, cinnamon stick, and peppercorns and toast until fragrant, 1 to 2 minutes. Add ginger, green onions, and garlic to spices and stir for 30 seconds to 1 minute, until aromatic. Pour in stock and bring mixture to a simmer. Add chicken, cover, reduce heat to medium-low, and allow broth to simmer slowly for 10 minutes. By now chicken should be cooked through and firm. Transfer chicken to plate and continue simmering broth, covered, for another 20 minutes.

Meanwhile, cook rice noodles according to package instructions. Drain and set aside.

Cut or shred chicken into bite-sized pieces and set aside. Finely chop remaining green onion into thin rounds and set aside with chicken.

Strain simmered broth through fine-mesh sieve into clean saucepan and discard solids. Stir fish sauce and coconut sugar into broth before setting saucepan back on stove over high heat, bringing broth to a boil.

Divide noodles, chicken, and green onion among 4 serving bowls. Ladle hot broth into bowls before garnishing with carrot, bean sprouts, cilantro, mint, slices of chili, and squeeze of lime. Serve immediately.