How to Make It
Make the gnocchi: In a small saucepan, bring the water to a boil with 2 1/2 tablespoons of the butter and 1 1/4 teaspoons of the salt. Immediately, reduce the heat to low, add the flour all at once and beat with a wooden spoon until the dough is thick and comes away from the side of the pan. Cook, stirring, to dry out the dough, about 30 seconds.
In a stand mixer, beat the dough at low speed until room temperature. Beat in the mustard and 1/4 cup of the cheese. Add the eggs, 1 at a time, beating until each is incorporated. Scrape the dough into a pastry bag fitted with a 1-inch tip or a small plastic bag and refrigerate until chilled, at least 10 minutes. Cut off a 1-inch corner from the plastic bag before proceeding.
Meanwhile, make the butter sauce: In a small saucepan, bring the water to a boil. Add 4 tablespoons of the butter and cook until melted. Reduce the heat to low and gradually whisk in the remaining 4 tablespoons of butter until it melts creamily. Remove the pan from the heat and season with fleur de sel and pepper. Keep warm.
Line a baking sheet with paper towels. Bring a large saucepan of water to a boil and season with salt. Reduce the heat to maintain a gentle simmer. Carefully hold the pastry bag over the water and press out the dough, using kitchen scissors to cut it into 1 1/2-inch lengths. When the gnocchi float to the top, cook them for 2 to 3 minutes. Using a slotted spoon, spread the gnocchi on the prepared baking sheet.
In a large nonstick skillet, melt the remaining 2 tablespoons of butter. Add the gnocchi and cook over moderate heat, turning once, until golden brown on both sides. Transfer the gnocchi to plates and spoon the butter sauce over the top. Shave cheese over the gnocchi, sprinkle with the parsley and chives and serve.