Set up your breading station with three bowls: lightly beat the eggs in the first bowl, combine panko, freshly grated Parmesan, and lemon zest in the second bowl, and place the salt and pepper in a small dish. Pound the chicken breasts to an even 1/2-inch thickness—this ensures they cook uniformly and stay tender. Pat the pounded chicken dry with paper towels to help the coating adhere better.
Working with one chicken breast at a time, season both sides lightly with salt and pepper, then dip into the egg mixture and coat thoroughly. Transfer to the panko mixture, pressing gently so the coating adheres evenly. Heat the olive oil in a large skillet over medium-high heat until shimmering, then carefully place the breaded chicken cutlets in the pan. Cook for 5 minutes on the first side until golden brown, then flip and cook for another 5 minutes until the internal temperature reaches 165°F. The panko will turn a deep golden color—this is where the crunch and flavor come from.
Transfer the cooked chicken to a serving plate and keep warm. In the same skillet, reduce heat to medium and add the butter and minced garlic. Cook for about 30 seconds, stirring constantly, until the garlic becomes fragrant—don't let it brown or it will taste bitter. Pour in the chicken stock and fresh lemon juice, then add a pinch of pepper and stir to combine. Simmer the sauce for 2 minutes to let the flavors meld together. I like to use fresh lemon juice squeezed just before cooking because it gives the sauce a brighter, more vibrant acidity that bottled juice simply can't match.
Return the cooked chicken cutlets to the skillet and gently coat them with the lemon-butter sauce, turning to ensure both sides are well coated. Plate the chicken and drizzle any remaining sauce over the top. Garnish generously with fresh chopped parsley for a pop of color and fresh flavor. Serve immediately while the chicken is still warm and the sauce is at its best.