Heat oven to 200 degrees. Cut each chicken breast in half horizontally to make thin cutlets. Press with heal of your hand to flatten.
Put 2 T. olive oil in a large skillet over medium heat.
Set up 3 shallow bowls for dredging; fill one with flour, one with bread crumbs, and crack eggs into the last bowl and beat them. Season all with salt and pepper.
Dredge the chicken cutlets one at a time in flour, then egg, then crumbs. As you finish the cutlets, put in skillet. Raise the heat to medium high.
Cook cutlets until they are browned, 3 or 4 minutes. Turn and cook on other side until cooked through.
As the pieces finish, transfer to oven to keep warm. Continue frying cutlets, adding more oil as necessary.
Chop 1/4 c. parsley leaves.
Transfer all cutlets to oven; add wine to skillet and cook until it's reduced by about half.
Add chicken stock along with accumulated juices around chicken; cook until sauce thickens a bit, 2 or 3 minutes.
Stir in butter; squeeze in lemon juice. Stir in parsley and cook. Taste and adjust seasonings. Pour over cutlets and serve.