Cut the chicken breasts in half lengthwise. Lightly pound them to an even thickness.
Whisk together the eggs, garlic, Italian seasoning, salt, and pepper in one bowl. Combine the Parmesan and flour in another bowl.
Dip each piece of chicken in the egg mixture, then dredge it in the Parmesan mixture, allowing excess coating to fall away.
Heat enough olive oil to cover the bottom of a large nonstick skillet. Cook the chicken for 4 to 5 minutes per side, until golden, crisp, and cooked to 165°F (74°C). Reduce the heat if the coating browns too quickly.
Meanwhile, melt the butter with the garlic in a separate saucepan and cook until fragrant. Add the chicken broth, lemon juice, and pepper; cook over medium heat for about 2 minutes.
Pour the sauce over the cooked chicken and turn to coat. Garnish with lemon slices and parsley, if desired.
