Place steaks on a clean work surface and pound both sides to 1/4-inch thickness with the tenderizing side of a meat mallet. Season steaks with 1 teaspoon salt and 1/4 teaspoon pepper.

Combine 1 cup flour and cayenne pepper in a wide, shallow dredging bowl and pour buttermilk into another dredging bowl. Coat steaks in flour, then buttermilk, and again in the flour. Transfer to a baking sheet lined with a cooling rack and let stand 20 minutes.

Pour oil to 1/8-inch depth into a large cast-iron skillet and heat over medium-high heat. When oil shimmers, fry the steaks in two batches, turning once, until golden brown on both sides, about 3 minutes per side. Transfer to a paper towel-lined plate to drain.

Carefully pour all but 2 tablespoons of fat from skillet and return skillet to heat. Whisk in remaining 3 tablespoons flour, cooking until bubbly and golden, 1 minute. Whisk in milk and season with remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Boil, whisking constantly, until gravy thickens slightly, 1 minute. Transfer to a gravy boat or small pitcher and serve immediately poured over steaks.