Preheat oven to 400°F.
For the Gougères, in a medium saucepot over medium-high heat, combine water, butter and salt. Heat until butter has melted and water is boiling.
Add flour and cook, stirring constantly with a wooden spoon. Stir until mixture begins to create a dough ball in the center of the pot and the dough is completely pulling away from the sides of the pan, about 2 minutes.
Transfer mixture to a mixing bowl or the bowl of a stand mixer fitted with a paddle attachment. On low speed, add the eggs to the mixture one at a time, scraping the sides of the bowl well after each addition and beating until the bowl feels cool (the mixture should be very smooth and silky). Add in the herbs and cheese after the last addition of the eggs.
Transfer the mixture to a plastic food storage bag and cut half an inch off of one corner to create a pastry bag. On a baking sheet lined with parchment paper, squeeze the mixture into small rounds and bake until golden brown and puffed, about 25 minutes.
(The pastries can be made a day or two ahead of time and kept in an airtight container at room temperature. If they feel soggy when you take them out, pop them into a 400°F oven for a couple of minutes until they crisp up again.)
For the Mortadella Mousse, add the mortadella to the bowl of a food processor and pulse until almost a paste. Add the mascarpone, balsamic, heavy cream and pepper, and process until smooth.
Place mixture in plastic food storage bag and cut off corner to make a pastry bag or pipe from a pastry bag with wide mouth scalloped tip.
Cut gougères in half crosswise and fill with mortadella mousse. Roll sides of gougères in toasted pistachios, arrange on a platter and serve.
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