Char the onions and ginger: Preheat broiler to high. Place onion and ginger cut-side-up on a baking sheet, brush with oil, and broil for 7-10 minutes until slightly charred. Set aside.

Prepare the broth: In a large stockpot, toast star anise, cloves, cinnamon, cardamom, and coriander seeds over medium-high heat for 3 minutes until fragrant. Add charred onion, ginger, and vegetable stock. Bring to a simmer, then reduce heat to medium-low, cover, and simmer for at least 30 minutes.

Strain and season broth: Strain out and discard the onions, ginger, and spices from the broth. Stir in brown sugar, soy sauce, and rice vinegar. Taste and season with salt as needed. Keep simmering on medium-low, covered, until ready to serve.

Cook noodles: While the broth simmers, cook pho noodles al dente according to package instructions. Drain, rinse with cold water, and toss with a drizzle of sesame oil to prevent sticking.

Sauté vegetables: Heat oil in a sauté pan over medium-high heat. Add sliced mushrooms and sauté for 5 minutes until cooked and lightly golden. Five minutes before serving, stir the cooked mushrooms and bok choy into the hot broth to briefly cook.

Assemble and serve: Add a handful of noodles to each serving bowl. Ladle hot broth and vegetables over the noodles. Top with fresh garnishes and a generous squeeze of lime juice. Serve immediately, encouraging guests to stir in garnishes and add extra sauces if desired.