In a shallow pan or plate, sift together flour, salt, and pepper. In another shallow pan, combine egg and water. In still another shallow pan, place baking mix. Coat steak pieces in flour mixture, dip in egg mixture, and then coat with baking mix.
In a large frying pan over medium-high heat, add vegetable oil and heat until a drop of water sizzles. Add coated steak pieces, in batches, and fry 4 to 5 minutes per side or until golden brown and thoroughly cooked, add additional vegetable oil if needed. Remove from pan and keep cooked steaks warm in preheated oven (150°F). Pour off all but 2 tablespoons of the cooking oil. Put the frying pan back over the heat and make the gravy.
In the same frying pan with 2 tablespoons pan drippings, over medium heat, sprinkle flour over the oil and blend with a wooden spoon or whisk until smooth. Whisking or stirring constantly, slowly pour in milk, cream or evaporated milk; continue stirring, scraping loose browned bits from the bottom and sides of skillet, until the gravy begins to boil and thicken. Season with salt and pepper to taste.
Reduce heat to low and simmer, stirring occasionally, 5 to 8 minutes or until gravy is thickened to the desired consistency and the flour has lost its raw, pasty taste. Remove from pan and serve hot with the steak strips.