For the mousse: Combine the mortadella, ricotta and pepper in a food processor and process until mostly smooth. Add the Parmigiano and Marsala, and process into a very smooth purée. Add the butter and process briefly to fully incorporate. Taste and adjust the seasoning if necessary, although the saltiness of the mortadella usually does not require any additional salt.
For the gougeres:
Chill for 1 hour before using. It will keep in an airtight container in the refrigerator for up to 2 days.
Preheat the oven to 400°F. Line a baking sheet with parchment paper.
In a large, heavy-bottomed saucepan, combine the milk, butter, salt and pepper over medium-high heat. Bring to a boil, then remove from the heat, add the flour all at once, and stir briskly with a wooden spoon for about 1 minute to incorporate. Return to the heat and continue stirring until the batter thickens, comes together in a ball and pulls away from the side of the pan, about 1 minute.
Turn off the heat. Add the eggs, one at a time, beating until each egg is completely incorporated before adding the next one. Stir in the cheese until it is incorporated.
Drop the dough by teaspoon (or transfer it to a pastry bag fitted with a plain tip and pipe mounds approximately 1 inch in diameter) onto the prepared baking sheet, leaving about 1 inch of space between each. Bake for 10 minutes, then reduce the oven temperature to 325°F and bake until golden brown, 20-25 minutes. Allow to cool on the baking sheet for 5 minutes, then transfer to wire racks to cool completely.
Once cooled, cut the tops off the gougeres using a sharp serrated knife and, if necessary, use your fingers to pull out any soft dough from the center. Just before serving them, use a piping bag or small spoon to full the centers of the gougeres with the mousse, then place the tops back on, as if setting a little hat on top.