Pound the chicken cutlets to an even 1/2-inch thickness and season them with 1 tsp salt and 1/2 tsp pepper.
Whisk 1 1/4 cups flour with the paprika and garlic powder in a shallow dish; whisk the egg and buttermilk in a second dish.
Dredge each cutlet in flour, dip it in buttermilk and press it firmly into the flour again, then rest the coated pieces on a rack for 10 minutes.
Heat the oil in a cast-iron skillet to 350°F and fry two cutlets at a time until deep golden and 165°F inside, 3 to 4 minutes per side.
Transfer the chicken to a rack, pour off the oil and return 3 tbsp of the browned frying fat to the skillet.
Whisk the remaining 1/4 cup flour into the fat over medium heat for 1 minute, then slowly whisk in the milk.
Add the remaining 1/2 tsp salt and 1/2 tsp pepper and simmer until the gravy coats the back of a spoon, 4 to 5 minutes.
Spoon the gravy around, not over, the chicken until serving so the crust stays crisp.
