Step 1Heat 2 tablespoons butter in a large skillet until melted and bubbly. Add the chicken livers and cook over medium-high heat until browned, 2 to 3 minutes, then turn and add the onion. Continue cooking, stirring, until the chicken livers are almost cooked through, 3 to 4 minutes.
Step 2Add the chicken broth and bring to a simmer. Cook until the livers are cooked through and the liquid is reduced by half, about 5 minutes.
Step 3Spoon the livers and onion into the bowl of a food processor, along with the salt, black pepper and Cognac, and puree until smooth. Cut up the remaining stick of butter and add bit by bit to the liver, continuing to puree until smooth and blended. Spoon the liver mixture into a bowl. Cover and refrigerate until it firms up enough to pipe through a tube.
Step 4Using a pastry bag fitted with a filling tube, make a small opening in the side of each slightly cooled gougere and pipe in the mousse. Refrigerate any leftover mousse to serve as a spread along with baguette slices or small toasts.