Line baking sheets with parchment paper. Preheat oven to 375° F.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.
Using 2 teaspoons form dough into 1 ½ inch ovals, drop into baking sheet 1-inch evenly spaced apart. Place the baking sheet in the middle of the oven. Bake until golden, about 20 minutes. Serve immediately.