Trim green tips from lemongrass and peel off tough outer layer from each. Mash stalks with a meat mallet or rolling pin, then tie each stalk in a knot. Put in a small pot, add chicken broth, serrano chile, shallot, and ginger, and bring to a boil over high heat. Reduce heat to medium and simmer 10 minutes.
Remove lemongrass, serrano chile, and ginger from pot and discard. Add zucchini, mushrooms, jalapeño chile, and shrimp. Turn off heat and let steep until shrimp is just cooked through, 2 minutes.
Stir in fish sauce, 1 tbsp. vinegar, the cilantro, and dill. Add more vinegar to taste, if you like.
Divide among 4 bowls and serve hot.