Skin and bone chicken breasts, removing all fat, sinew and tendons. With palm of your hand flatten each breast half on work surface. Holding a very sharp knife parallel to work surface, slit each half breast in two. Put fillets between two long sheets of wax paper, cut side up. Pound them with flat side of a heavy cleaver until almost transparent. Peel off top paper.
Cut cheese into 8 even sticks. Place 1 stick, slightly diagonal on each piece of chicken. Sprinkle with 1/8 each of herbs and garlic; season with salt and pepper. Carefully roll up each piece of chicken, completely enclosing cheese. Seal ends by tucking them in or pressing them together. Dust each roll lightly with flour, brush with egg and roll in panko. Fry in oil heated to 350 degrees F until golden brown, 4 to 6 minutes. Drain on paper towels. To serve, arrange on a hot napkin on a warmed serving plate and garnish with crisp watercress.