In a small pan over medium heat melt the butter. Let the butter turn golden then toasty brown. Take off the heat and transfer to a heat proof bowl to stop the cooking.
Place the mortadella and Parmigiano in a food processor and process until smooth. Add the warm butter and continue processing until silky.
Taste and adjust for seasoning, adding a bit of nutmeg, black pepper and shaved truffle if you like.
Form the butter into a log and roll tightly in plastic wrap. Refrigerate the butter until you are ready to serve.