Place chicken breasts between plastic wrap and pound to ¼-inch thickness. Season both sides with salt and pepper, letting the flavors penetrate the meat for at least 5 minutes.

Place flour in one shallow dish and beaten eggs in another to set up your dredging station.

Dredge each piece first in flour, shaking off excess, then dip completely in beaten eggs. Let any excess egg drip off before cooking.

Heat olive oil and butter in a large skillet over medium-high heat. When the butter stops foaming, add chicken pieces without overcrowding. Cook 3-4 minutes per side until golden brown and cooked through. Transfer to a plate and cover loosely.

In the same pan, add white wine and lemon juice, scraping up any browned bits. Let it simmer for 2 minutes, then whisk in cold butter one piece at a time until sauce coats the back of a spoon.

Return chicken to the pan, spooning sauce over each piece. Sprinkle with fresh parsley and arrange lemon slices on top.