Pound chicken breasts to an even 1/2-inch thickness using a meat mallet.
Prepare a breading station with three shallow bowls: the first with 1/4 cup flour, the second with beaten eggs, and the third with panko mixed with herbs, salt, and pepper.
Dredge each chicken breast in flour, dip in egg wash, then press firmly into the herb-panko mixture to coat thoroughly.
Heat olive oil in a large skillet over medium-high heat.
Sear chicken for 5 to 6 minutes per side until the crust is golden brown and the internal temperature reaches 165 degrees Fahrenheit (74 degrees Celsius). Remove chicken from skillet and tent with foil.
Melt 2 tablespoons of butter in the same skillet over medium heat and sauté minced garlic for 60 seconds.
Whisk in the remaining 1/4 cup of flour and cook for 1 minute to form a light roux.
Gradually whisk in chicken stock and heavy cream, simmering until the sauce thickens to a gravy consistency.
Whisk in the remaining 2 tablespoons of butter until the sauce is glossy and smooth.
Serve the garlic butter gravy immediately over the rested herb-crusted chicken breasts.