Place the chicken livers and milk in a medium bowl, cover, and refrigerate for at least 2 hours. Drain the livers and discard the milk.
Melt 4 tablespoons of the butter in a medium (10-inch) skillet over medium heat. Add the onion and cook for 8 to 10 minutes, stirring occasionally, until tender but not browned. Add the chicken livers and thyme and cook for 4 to 5 minutes, turning with tongs to cook evenly, until they're lightly browned on the outside but still raw inside. Add the Cognac, 1 tablespoon salt, and 2 teaspoons pepper and continue to cook for 3 to 4 minutes, until the livers are cooked but still very pink inside. (If they're overcooked, the pate will be dry.) Pour the contents of the pan into the bowl of a food processor fitted with the steel blade and allow to cool for 15 minutes.
Pulse the processor until the chicken livers are almost smooth. Dice the remaining 4 tablespoons of butter and add to the bowl. Add the truffle butter and process until smooth. Add the parsley and pulse just to incorporate.
Pour the mousse into one large or four small (8-ounce) ramekins. Pour a thin layer of melted duck fat or clarified butter on each mousse and place whole parsley sprigs on top. Refrigerate for at least 6 hours. Allow to sit at room temperature for 15 minutes before serving with crackers or warm toasts.
For filming, Ina used an 8 1/2 x 4 1/2 x 2-inch loaf pan lined with plastic wrap instead of ramekins.
This recipe has been updated and may differ from what was originally published or broadcast.