Pat dry the chicken breasts and season lightly with salt on both sides.
On a plate, mix together the all-purpose flour, panko breadcrumbs, Italian seasoning, salt and black pepper.
Dredge the chicken pieces in the seasoned breading mixture.
In a large skillet, over medium-high heat a few drizzles of olive oil. Fry the chicken pieces in batches being careful not to crowd the pan. Depending on the thickness, this should take around 3-4 minutes per side or until the juices run clear. Remove to a platter and keep warm.
After all of the chicken is cooked, add 2 Tbsp of butter to the pan. Add additional olive oil, if needed. Saute the sliced onion, mushrooms, minced garlic, rosemary and red pepper flakes.
Cook over medium for 8-10 minutes or until the juice has released from the mushrooms and has evaporated. Season with salt and black pepper to your taste.
Add the chicken broth, balsamic glaze or vinegar and granulated sugar to the pan. Stir well scraping any brown bits from the bottom of the pan.
Cook over medium-high for 3 minutes or so until the sauce has reduced and slightly thickened. Return the chicken to the pan.
Serve drizzled with the sweet balsamic mushrooms and onions and a sprinkling of fresh parsley.