Pat steaks dry and season both sides with salt and pepper. Using a meat mallet, pound each steak to about 1/4-inch thickness.
In a shallow dish, combine 1 cup flour, seasoned salt, 1 teaspoon black pepper, garlic powder, and cayenne pepper. In another dish, whisk together eggs and 1/4 cup milk.
Dredge each steak in seasoned flour, then dip in egg mixture, then back in flour, pressing to adhere.
Heat oil in a large skillet over medium-high heat until shimmering. Fry steaks for 3-4 minutes per side until golden brown and cooked through. Transfer to a plate.
Reduce heat to medium. Add 1/4 cup of the remaining flour to the pan drippings and whisk for 1 minute.
Gradually whisk in 2 1/2 cups milk, scraping up browned bits from the bottom of the pan.
Cook, stirring frequently, until gravy thickens, about 5-7 minutes. Season generously with black pepper and salt to taste.
Serve steaks smothered with the white pepper gravy.