In a baking dish or shallow bowl, beat the eggs with the parsley and season with salt and pepper. In another shallow bowl, mix the flour with the thyme. Season with salt and pepper.
Season the chicken with salt and pepper. Dredge the breasts in flour first, shaking off any excess, then dip in the egg wash. Transfer to a plate.
In a large skillet, melt the butter, or warm the olive oil if using, over moderate heat. Add the chicken and cook over moderate heat, turning once, until golden brown and cooked through, about 3 minutes on each side. Transfer to a plate.
Add the white wine to pan to the pan and cook until reduced, then add the chicken stock and lemon juice. Season with salt and pepper.
Remove chicken and reduce sauce. Replace chicken in pan and simmer.
Serve over angel-hair pasta with a side of sautéed green beans. Garnish with sliced lemon.