Heat oven to 350°. Lay chicken breasts between sheets of plastic wrap and pound gently with flat side of a meat mallet to ½-inch thickness.
In a shallow casserole or pie plate, beat eggs. In a separate casserole or pie plate, combine bread crumbs, cheese, herbs, salt, and pepper. In batches, coat chicken breasts with egg, shaking off excess. Add to bread-crumb mixture and press to coat chicken. Set aside on a plate; cover and refrigerate 30 minutes.
Pour ¼ inch oil into a large saute pan. When oil is shimmering but not smoking, add chicken breasts to pan (don’t crowd them) and fry 2 to 3 minutes on each side. Place on a baking sheet and bake 10 minutes.
Sprinkle with Parmesan cheese and serve with meatballs and sauce.