Slice the chicken breasts in half horizontally. Place them between two sheets of plastic wrap and pound them with a meat mallet until they are 1/2-inch (1.25 cm) thick.
In a shallow bowl, whisk the eggs, 1 clove of minced garlic, Italian seasoning, salt, and 1/4 teaspoon of black pepper.
In a second shallow bowl, stir the Parmesan cheese and flour together.
Dip each piece of chicken into the egg mixture, letting the excess drip off. Press the meat into the cheese mixture to coat both sides.
Heat the olive oil in a large non-stick skillet over medium-high heat. Add the coated chicken and cook for 4 to 5 minutes on the first side.
Flip and cook for another 4 to 5 minutes until golden brown. The thickest part must reach an internal temperature of 165°F (74°C). Transfer the meat to a serving platter.
In a separate small saucepan, melt the butter over medium heat. Add the remaining 2 cloves of minced garlic and cook for 1 minute until fragrant.
Pour the chicken broth, lemon juice, and the remaining 1/4 teaspoon of black pepper into the saucepan. Simmer for 2 minutes.
Pour the warm sauce over the cooked chicken. Top with lemon slices and fresh parsley before serving.