In a medium saucepan, bring water, butter, and salt to a boil over high heat.
Add all the flour at once, stirring vigorously with a wooden spoon until a smooth dough forms.
Reduce heat to medium-low and continue to stir, cooking until the dough pulls away from the sides of the pot and forms a thin film at the bottom.
Remove from heat. Stir in mustard and Parmesan cheese until well combined. Add eggs one at a time, fully incorporating each before adding the next. Stir in parsley and chives.
Transfer the dough to a pastry bag with a 1/2-inch tip. Bring a large pot of salted water to a simmer. Pipe the dough into the simmering water, cutting into 1-inch pieces.
Cook until gnocchi float to the surface, then continue to cook for about 2-3 minutes more.
Remove gnocchi with a slotted spoon, transfer to a baking sheet, and drizzle with olive oil. Toss to coat and serve hot, sprinkled with additional herbs.