Cut the chicken breasts in two down the middle and trim away fat and membranes. Pound the chicken breasts, smooth side down, between 2 pieces of waxed paper, to about 3/8 inch thickness.
Combine eggs with milk in a shallow bowl and beat well. Spread fresh breadcrumbs (I use about 1 loaf of bread in the food processor) on a sheet of waxed paper.
Dip chicken cutlets in egg mixture, then in crumbs, pressing them firmly with your fingers to make them adhere. If you have time, refrigerate them for an hour or so on a waxed paper-lined cookie sheet to firm the coating.
Heat butter in a large skillet and when hot and bubbling, add as many cutlets as will fit in one layer without crowding. If the cutlets are crowded, they will steam instead of saute. Brown quickly on both sides, sprinkling with salt and pepper as they cook. Each side will take no more than 2-3 minutes, just until the coating is lightly browned. Add more butter between batches if needed. Keep the cooked cutlets warm.
When all are done, reduce heat under the skillet. Squeeze the juice of one lemon into the pan drippings. Stir in chicken broth, scraping pan to loosen browned bits from the bottom. Simmer for 15 minutes. Taste and correct seasoning.
Pour sauce over cutlets and serve with a sprinkling of chopped parsley and thin slices of lemon over top.