Preheat oven to 375ºF and have a sheet pan lined with parchment paper or silpat ready. You will also need a pastry bag with an #8 plain piping tip for both the gougères and the filling.
Add the water, milk, sea salt, and EVOO to a 3 quart saucepan
Bring the mixture to a boil on a medium high heat
Lower the heat to medium and add the flour all at once and stir with a wooden spoon. Keep stirring until the mixture comes away from the sides and bottom of the pot and forms a dough ball. Keep stirring for about 3 minutes to dry the dough out a little; it should be stiff enough to keep its shape.
Place the dough in the bowl of a stand mixer with a paddle attachment. Beat on a low speed to cool the dough a little. You want the dough to be very warm, but not hot.
Switch to a medium speed and slowly add the beaten eggs a little at a time. With each addition wait for the eggs to incorporate into the dough. You are looking for shiny dough that keeps its shape when piped onto a sheet pan. Too many eggs, and they will not hold their shape when piped; too few eggs, and the gougères will not puff. This is why the eggs should be beaten beforehand—there are too many variables in egg sizes and dough moisture levels to know ahead of time how many eggs will be just right so, once again, you are looking for a shiny dough that keeps its shape when piped onto a sheet pan.
Add 2 oz of the Gruyère to the dough and mix until well incorporated.
Fill the pastry bag with the finished dough and pipe 1 ½” rounds onto the parchment covered pan leaving about 2” between each one to allow room to puff. Keep the bag at 90º and lift slowly as you pipe. Tap down the top of each dough mound with a wet finger to flatten it.
Sprinkle the remaining 1 oz of Gruyère over the piped gougères
Bake for approximately 30 minutes or until they’re golden brown and dry enough to hold their shape. Take them out of the oven and turn off the heat. Poke the sides of the gougères with a small paring knife to let out the steam, then put them back in the (now turned off) oven to dry out.
While the gougères are continuing to dry, start on the filling beginning with the Duxelles
Chop the mushroom finely, either by hand or with a food processor
Add 2 Tbsp of the EVOO to a sauté pan on medium heat, and when it shimmers add the finely chopped mushrooms and cook until their water has evaporated.
Add 2 more Tbsp of EVOO and the minced shallots. Cook for 5 more minutes.
Add the wine and fresh herbs. After the wine has evaporated, turn off the heat and hold for inclusion in the Mornay sauce, below.
The gougères are continuing to dry, and the Duxelles complete, start on the Mornay sauce by melting the butter in a saucepan on medium heat until the butter foams.
Add the flour and whisk to incorporate, creating a roux. Continue to whisking cooking the roux for 3 minutes.
Add the milk and continue to whisk, cooking the mixture until it simmers and thickens. Cook for 3 more minutes…you now have a Béchamel, (one of France’s 5 mother sauces).
Stir in the grated Gruyère and continue to stir until melted, transforming your Béchamel into a Mornay sauce.
Stir in the Duxelles, and salt and pepper to taste
Let the mixture cool a little before piping
Remove the gougères from the oven, and slice the top third off with a serrated knife.
Pipe the filling you’ve prepared into the gougères while both are still warm.
