In a stockpot, combine the liquid ingredients. Split the lemongrass in half and whack both pieces with the back of a knife and add to stock, along with ginger and lime leaves. Bring to a simmer. Cover and steep 10 minutes to hep the flavors to infuse.
Add fresh matsutake, onion, baby bok choy, and jalapeño. Bring up to a simmer and reduce heat to low. Continue to simmer for 5 minutes or until onions and book chop turn tender. Add fish sauce, if using, and then salt to taste.
Take off heat and add lime zest and juice to taste, and garnish with lime wedges, cilantro, and jalapeño.