Preheat oven to 420 degrees F. Either line a baking sheet with parchment paper or with the non-stick baking mat. Do not grease the baking sheet, as the grease will cause the dough to flatten.
NOTE: Prepare all your ingredients in advance, as preparation will go quickly once you start cooking. This is called Mise en Place - What Is A Recipe.
In a small bowl, combine flour, cayenne pepper, dry mustard, and salt; set aside.
In a small bowl, add eggs and egg whites; whisk until mixed together; set aside.
Cut up butter into small pieces; set aside.
Grate Gruyere and Parmesan cheeses; set aside.
In a heavy saucepan over medium-high heat, combine the water and butter; bring mixture to a full rolling boil (make sure the butter has all melted). Remove pan from the heat and add flour mixture all at once, stirring vigorously with a wooden spoon until blended. NOTE: The flour absorbs the liquid rapidly, and must be mixed thoroughly until there are no lumps left.
Reduce heat to medium; return pan to heat and continue stirring until the mixture leaves the sides of the pan and forms a ball, stir approximately 30 seconds to 1 minute to evaporate excess moisture. Remove from heat and transfer the dough to the bowl of an electric mixer.
Using your mixer with the paddle attachment, mix at low speed until the dough has cooled slightly. It should be about 140 degrees F. (use your digital thermometer to test the dough).
At medium speed, beat the eggs/egg whites mixture in a little at a time. Add no more than a quarter of the eggs at once; wait until eggs are completely absorbed before adding more (at first the eggs will act like they do not want to mix in, but they will). When all the eggs are absorbed, the dough is ready to use. The dough should be soft and a little sticky, but be able to hold its shape. Stir in the grated Gruyere and Parmesan cheeses until well incorporated.
Time to make the Gougeres - Following are some of the different techniques that people use to form the balls of dough:
Using two teaspoons: With one spoon, scoop up about 2 to 3 teaspoons for a cocktail-size puff (walnut size). With other spoon, push batter off first spoon and drop in a mound onto prepared baking sheet.
Using plastic bag: Place dough into bag. Cut the end off one corner with scissors, to make an opening about 1/4 inch. Squeeze the mixture onto the pans.
Cookie scoops: Cookie scoops can also be used.
Using pastry bag: Put a 1/4-inch star tip into your pastry bag. Fill the bag with the dough. Squeeze the dough out in a circle motion to create small silver dollar-sized circles.
Finger and spoon: This is how I do it. It is easy and goes fast.
Leave about 2 inches between each gougere on the baking sheet, as the mixture will spread during baking. Do not worry if they do not look neat, they tend to round out as they rise in the oven. To smooth out any parts that stick up when you squeeze out the dough, just wet your finger in water or milk and smooth out.
When gougeres are ready to bake, sprinkle a few some coarse salt on top of each gouge.
Bake for a total of about 18 to 20 minutes, rotating the pans halfway through (switch pans so the top one is on the bottom rack and vice versa). Do not overcook the gougeres, they are better when slightly under cooked. Remove from oven, using a thin spatula remove from baking sheet, and let cool slightly before serving.
Makes approximately 36 gougeres.
* Bread flour is a high-protein flour. The high protein gives you more gluten and structure and helps the cream puffs rise. All-purpose flour may be substituted but the results will not be as spectacular.
** The egg whites help the puffs to be more dry inside.
The dough can be prepared 2 to 3 hours in advance. Make the dough balls, cover, and refrigerate. When ready to bake, remove from refrigerator, and bake them into a preheated oven.
The dough may be made a day ahead and kept covered in the refrigerator. When ready to use, remove from refrigerator, make balls, and then bake in a preheated oven.
You may also bake and freeze them. Thaw at room temperature and refresh in a 350 F. oven for about 10 minutes.
For best results, use puffs with 24 hours, or wrap airtight and freeze.
If you are making and baking gouges ahead of time, poke the bottoms after you remove them from the oven, turn upside down, and let dry out on the baking sheet.
Gougeres are easy to travel with to. You can bring them to a dinner party and re-heat them (5 minutes at 350 degree F.) on a baking sheet when you arrive.
Blue Cheese or Cheddar Cheese may be substituted for the Gruyere cheese. Actually any hard cheese may be substituted.
Gruyere Cheese Gougeres Recipe: https://whatscookingamerica.net/appetizers/gougeres.htm