Beat together the egg and milk and set aside.
Mix together the salt, black pepper, paprika and white pepper and sprinkle on both sides of beef cutlets.
Dredge the cutlets in the flour, shaking off the excess.
Then dip each cutlet in the egg/milk mixture, then back in the flour. (You're going to get your hands messy here, so take your rings off.)
Set cutlets aside on a piece of waxed paper.
Heat the cooking oil in a large cast-iron or other heavy skillet over medium-high heat for a few minutes.
Oil should be about a half-inch deep in the pan.
Check the temperature with a drop of water; if it pops and spits back at you, it's ready.
With a long-handled fork, carefully place each cutlet into the hot oil.
Protect yourself (and your kitchen) from the popping grease that results.
Fry cutlets on both sides, turning once, until golden brown.
Reduce heat to low, cover and cook 4 or 5 minutes until cutlets are done through.
Drain cutlets on paper towels.
After the cutlets are removed from the pan, pour off all but about 2 tablespoons of oil, keeping as many as possible of the browned bits in the pan.
Heat the oil over medium heat until hot.
Sprinkle flour in the hot oil.
Stir with a wooden spoon or whisk, quickly, to brown the flour.
Gradually stir in milk and water, mixed together, stirring constantly with the wooden spoon or whisk and mashing out any lumps.
Lower heat, and gravy will begin to thicken.
Continue cooking and stirring a few minutes until gravy reaches desired thickness.
Check seasonings and add more salt and pepper according to your taste.