Bring water, butter and salt to a rolling boil in a medium saucepan. Remove from heat and stir in the flour.
Return to medium heat and stir with a wooden spoon until the batter pulls away from the sides of the saucepan, about 1-2 minutes.
Transfer the batter to a stand mixer fitted with the paddle attachment. Mix on low speed for 1 minute, then increase to medium speed and add six eggs one by one. Reserve the last egg for brushing.
Add the grated cheese and herbs and combine well. Pour the batter into a piping bag fitted with a star tip or round tip, or freezer bag with the corner snipped off. Pipe the batter into small rounds onto a ungreased sheet pan and freeze for at least one hour.
Preheat the oven to 425 degrees. Remove gougères from freezer and brush with beaten egg. Bake 10 minutes.
Open the oven door, rotate the baking sheet and bake another 10 minutes, until golden brown. Serve warm or at room temperature.