Place the cheeses, softened butter, parsley, tarragon, 1/2 teaspoon pepper and 1/4 teaspoon salt in a bowl. Beat and mash the ingredients together until they form a stiff paste - your fingers or a big wooden spoon are the best tools for this job. Divide the mixture into four finger-shaped logs, each about 3 inches long. Set aside.
Flatten each chicken breast by placing it between two sheets of plastic wrap or waxed paper and pounding with a mallet or rolling pin until roughly 1/4-inch thick and 5 or 6 inches across. Season the chicken lightly with salt and pepper.
Place a cheese log in the center of each breast, then roll and fold the chicken around the cheese to enclose it completely.
Preheat oven to 350 degrees.
Place a sheet of phyllo dough on your work surface. Top with a second sheet and brush lightly with melted butter. Set a chicken breast in the center of one of the narrower ends, then roll it up in the phyllo, tucking the ends of the dough under to enclose the chicken and make a neat package. Form the remaining packages the same way. Place them folds down in a 13-by-9-inch baking dish and brush with remaining melted butter. Bake about 40 minutes or until sizzling and well browned. A meat thermometer inserted into the center of the chicken should read 170 degrees. Serves 4.