Butterfly the chicken breasts, then slice them down the center to create 2 cutlets each.

In a small bowl, combine garlic powder, paprika, cayenne, salt, and pepper. In a shallow bowl, whisk together the flour and 1 tablespoon of the spice mixture. In a separate shallow bowl, lightly beat the eggs.

Set a cooling rack inside a rimmed sheet pan.

Sprinkle the chicken with the remaining spice mixture. Dip the chicken into the egg, allowing excess to drip off, then press both sides into the flour mixture.

Transfer to the prepared rack to set for at least 15 minutes.

Pour 1 inch of vegetable oil into a large cast-iron skillet. Heat over medium-high. Add chicken and cook until golden, 3 to 4 minutes per side, then transfer to a paper-towel-lined plate.

Repeat with remaining chicken, adding more oil as needed to maintain 1 inch.

Make the gravy by melting the butter in a small saucepan, whisking the flour with ½ cup stock until smooth, and gradually whisking in remaining stock and milk until thick. Keep warm over low heat.

Drizzle the chicken with the gravy and serve.