Preheat oven to 375 degrees. Use a sharp knife to cut a pocket horizontally in the thickest side of each chicken breast, being sure not to cut all the way through.
Place one slice of provolone cheese in the pocket, topped with 1/4 of the mozzarella, and 1/4 of the six cheese Italian. Use toothpicks to close and secure the opening.
Drizzle chicken breasts with olive oil. Season with salt and pepper, oregano, thyme, basil, and garlic powder and use your fingertips to rub seasonings into the chicken.
In a large oven-safe skillet (see note) over medium-high heat, melt butter. Once almost melted, add the honey and stir until mixture bubbles. Add chicken and brown on each side for 2-4 minutes. Whisk together the balsamic vinegar and brown sugar, pour over chicken and cook 2 minutes longer.
Transfer pan/skillet to oven and bake for about 15-20 minutes until chicken is cooked through and cheeses are melted. Spoon balsamic sauce from the pan over the chicken, top with fresh basil if desired, and serve.
Notes
If you don't have an oven safe pan or skillet, you can do this in a normal pan and then transfer everything into a casserole/baking dish or pan for baking portion.