Begin by preparing the chicken. Place the chicken breasts between two sheets of plastic wrap and gently pound them to an even thickness of about ½ inch. Season both sides with salt and pepper.
Set up a breading station with three shallow bowls: one with flour, one with beaten eggs (seasoned with salt and pepper), and one with chicken broth combined with lemon juice.
Dredge each chicken breast in the flour, shaking off the excess. Then, dip it into the egg mixture, allowing the excess to drip off. Finally, dip the chicken into the lemon broth mixture.
In a large skillet, heat 2 tablespoons of olive oil and 2 tablespoons of butter over medium-high heat.
Once hot, carefully add the chicken breasts to the skillet in batches (if needed to avoid overcrowding). Cook for about 4-5 minutes on each side or until golden brown and cooked through. Use tongs to flip the chicken.
Remove the cooked chicken and place on a plate lined with paper towels to drain.
In the same skillet, lower the heat to medium and add the remaining butter. Once melted, pour in the chicken broth and lemon juice mixture. Stir to combine and bring to a gentle simmer.
Add the cooked chicken back to the skillet, spooning the sauce over the top. Allow it to heat through for about 2 minutes.
Remove from heat, sprinkle with fresh parsley, and garnish with lemon slices if desired.
Serve hot with your choice of side dishes.