Hold lemongrass stalks and halved white onion directly over a gas flame or under a broiler for 2-3 minutes until blackened in spots. Smash lemongrass with the side of a knife to release oils.
4 stalks lemongrass, 1 whole onion
Add charred lemongrass, onion, beef shank, pork hock, galangal, shrimp paste, and 12 cups water to a large stockpot. Bring to a boil over high heat, then immediately reduce heat to a bare simmer.
2 lbs beef shank, 1 lb pork hock, 4 stalks lemongrass, 1 whole onion, 3 slices galangal, 2 tbsp shrimp paste
Simmer gently for 2.5 to 3 hours, skimming foam every 15 minutes during the first hour. Keep broth at a bare simmer to maintain clear broth and tender meat. The beef shank should pull apart easily and pork hock meat should slide off the bone.
Remove beef shank and pork hock from broth and let rest for 10 minutes before slicing.
2 lbs beef shank, 1 lb pork hock
Add fish sauce to broth one tablespoon at a time, tasting after each addition until balanced. Strain broth through a fine-mesh strainer to remove solids, then return broth to the pot.
0.25 cup fish sauce
Soak rice vermicelli noodles in cold water for 10 minutes, then drain well.
1 lb rice vermicelli noodles
Divide soaked noodles among bowls. Top with sliced beef and pork, ladle hot broth over, and drizzle with chili oil. Serve immediately with bean sprouts, lime wedges, and fresh herbs on the side.
1 lb rice vermicelli noodles, 2 lbs beef shank, 1 lb pork hock, 3 tbsp chili oil
