Combine flour, salt, and pepper; measure out and reserve 1/4 cup flour mixture. Place remaining 1/2 cup flour mixture in a shallow dish. Pound steaks to 1/4-inch thickness; dredge in flour mixture, coating well on both sides and pressing flour into meat.
Heat 3 tablespoons oil in a large heavy skillet over medium-high heat. Dredge steaks again in any remaining flour mixture and fry until browned on both sides, adding 1 or 2 tablespoons additional oil to skillet if needed. Remove steaks and set aside. Add onion to skillet and sauté until lightly browned. Add water, stirring to loosen clinging particles.
Return steaks to skillet; cover and simmer 30 minutes or until tender. Remove steaks, reserving drippings in skillet. Add reserved 1/4 cup flour mixture, stirring until smooth. Cook until lightly browned, stirring constantly. Stir in milk with a wire whisk. Cook, stirring constantly, until thickened. Return steaks to skillet, turning to coat with sauce; simmer until hot.
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