Transfer the flour mixture to the bowl of a stand mixer and beat it with the paddle attachment for 1 minute. Beat in the eggs, one at a time until fully incorporated into the dough before adding the next. When all the eggs are incorporated, stir in the cheese and scallions, mix well.
Drop the batter by a scant tablespoonful onto the baking sheets, leaving 1 inch between them. Bake for 7 minutes. Reduce the oven temperature to 350°F and continue to bake until the gougères are golden brown, about 15 to 20 minutes.