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, about 3 inches long. Set aside.
Place chicken breast between two sheets of plastic wrap and pound with a mallet until about 1/4 inch thick and 5 or 6 inches across and season lightly with salt and pepper.
Place cheese log in center of each breast, roll and fold the chicken around the cheese to enclose log completely.
Preheat oven to 350 degrees.
Place a sheet of phyllo dough on your work surface. Lay a second sheet on top of that and brush with melted butter. Set chicken breast in the center of one of the narrower ends and roll it up in the dough, tucking the ends of the dough under to enclose the chicken and make a packet. Form the remaining packets the same way.
Place packets, folded side down, in 13x9 inch baking dish and brush with remaining butter. Bake about 40 minutes or until sizzling and well-browned.