I don’t serve it in my restaurant, but being Italian I grew up with it and make it at home often.
You asked how to improve the breading, but based on the recipe you posted you’re not breading it at all - you’re just dredging it in flour. I’ve never seen a chicken parm that wasn’t breaded, so I think that’s where your problem lies.
For a quick version, mix equal parts of Italian Style bread crumbs and grated Parmesan for your breading. Dip the chicken in beaten egg and the coat with the breading. Pan fry the breasts in olive oil. You’ll then layer them with mozzarella cheese, sauce and a sprinkle of parmesan. Finish in the oven until the cheese is melted.
If you want to make the breading from scratch, I use equal parts of panko bread crumbs and parmesan and season with kosher salt, pepper, and fresh parsley. (I use fresh oregano too, but that’s not really traditional.) You don’t need a lot of seasoning in the breading as the sauce will carry most of the flavor. Let the chicken taste like chicken.
If you want a “scratch” taste, definitely make your breading yourself. It will take 5 minutes - well worth it for an all fresh taste.
We take the pounded chicken ta-ta, dredged in seasoned flour (salt, pepper), then dunking into an egg wash, finally a good coating of seasoned bread crumbs. Deep fry till golden delicious.
Growing up italian as well, I agree that Chicken Parm is always pan fried using modiga (italian breadcrumbs). We usually fry it in butter. We never deep fried with flour. To get it thinner, I’d slice it in half rather than pound it out. Pounding it out seems to make it less juicy (IMO) and gives it a processed look and texture.
Not to say you couldn’t make a good flour-breaded and deep fried chicken parm - it’s just not the way I grew up with it. Try the pan frying with butter and see what you think