In large cast iron pan, heat oil and butter over medium heat. Add onions, thyme, rosemary, salt and peppa, gaalic, and sugar and sherry. Cook on medium heat for about 45 minutes depending on level of doneness desired. Onions should be a light to medium brown. Stir with increasing frequency throughout the process. Towards end, stirring should be pretty constant to prevent burning. Remove from heat and set aside.

Whip eggs, garlic, salt and pepper in small bowl or pan. In separate pan, add parm cheese, thyme, rosemary, and corn starch and combine. Drench slices of chicken in egg mixture and then pat parm mixture onto the chicken until well coated.

In same pan you used to cook onion, heat EVOO over medium high heat. Add all chicken at once, creating a layer on the bottom of pan. If needed, add a bit more EVOO to make sure there is enough to sautee each piece. Flip after about 4 – 5 minutes or when edges have turned light to golden brown. Cook for an additional 2-3 minutes. Remove from heat. Spread onions over the chicken in pan. Add beef broth and top pan with additional shredded Parmesan or Italian cheese on top if desired. Bake uncovered for about 25 minutes or until onions have turned a golden to dark brown.