Instructions

1. Bring a large wide pot of water to a boil over high heat. Meanwhile, put 1 cup cold water, 9 tbsp. of the butter, and 1 1⁄2 tsp. salt into a heavy medium saucepan and bring to a boil over high heat. Remove pan from heat, add flour all at once, and vigorously stir with a wooden spoon until mixture forms a smooth dough. Return pan to medium heat and cook, stirring constantly, until dough pulls away from sides of pan, about 30 seconds.
2. Transfer dough to the bowl of a standing mixer fitted with the paddle attachment. Beat in eggs, one at a time, on medium speed, making sure each egg is fully incorporated after each addition. Increase speed to high and beat dough for 30 seconds. Add parmigiano-reggiano, chives, parsley, chervil, and tarragon and beat well. Transfer dough to a pastry bag fitted with a L" plain tip.
3. Add 2 generous pinches salt to boiling water and reduce heat to maintain a gentle simmer. Working quickly over the simmering water, pipe out 1⁄4" of the dough, then dip a knife into the hot water and cut off extruded dough, allowing it to fall into the simmering water. Repeat piping and cutting process with about one-quarter of the dough. Cook gnocchi in simmering water until they float, then continue to cook them for 3–5 minutes more. Transfer gnocchi with a Chinese skimmer or a slotted spoon, draining them well, to a large wide dish. Add remaining 3 tbsp. butter and toss until well coated. Repeat piping, cutting, cooking, draining, and tossing-in-butter process 3 more times with remaining dough.