Flatten breasts to an even thickness. Season with italian seasoning spice mix. Place 1 ham slice over each chicken breast, roll, and fasten with toothpicks. Melt butter in a medium skillet over medium high heat and fry chicken for 5 to 7 minutes, turning often to brown evenly, until almost cooked through (juices run clear).
Pour wine over chicken and allow to evaporate; place 1 cheese slice over each chicken breast and cover skillet. Cook until cheese has melted, about 5 minutes.