Bring 1 cup of water, butter, and ½ teaspoon salt to boiling in a heavy medium saucepan. Remove from heat and mix in the flour. Stir over medium heat until the mixture starts to become thick and begins to separate from the pan, about 3 minutes.
Transfer to a stand mixer fitted with a paddle. Add the eggs to the mixture, one at a time, mixing vigorously to form a sticky dough. Stir in cheese and scallions until well incorporated in the dough.