If the chicken breasts are thick, slice them horizontally or pound them until they are an even 1/2-inch thickness. Season both sides with the kosher salt and black pepper.

Place the all-purpose flour in a shallow dish and lightly dredge each chicken breast. Shake off excess flour so the coating stays thin and does not make the pan sauce heavy.

Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the chicken and cook for about 4 to 5 minutes per side, depending on thickness, until golden brown and the center reaches 165°F (74°C).

Transfer the cooked chicken to a plate and reduce the skillet heat to medium. Add the remaining tablespoon of butter and sauté the minced garlic for about 30 seconds, just until fragrant.

Pour in the chicken broth and fresh lemon juice, scraping the browned bits from the bottom of the skillet. Simmer for 2 to 4 minutes, until the liquid has reduced slightly.

Stir in the lemon zest and optional capers. Keep the sauce at a gentle simmer rather than a hard boil so the lemon flavor remains fresh and pleasant.

Return the chicken and any accumulated juices to the skillet. Spoon the sauce over the chicken and simmer briefly for about 1 to 2 minutes, allowing the meat to warm through and absorb the sauce.

Garnish with chopped fresh parsley and serve immediately. Spoon extra lemon sauce over each portion and pair it with rice, potatoes, noodles, bread, or a green vegetable.