For the steak fingers: Combine the flour, seasoned salt, pepper and cayenne in a dish. Whisk together the milk and eggs in a separate dish.
To bread the meat, first dredge in the flour mixture, then dip quickly in the egg mixture and then put back into the flour mixture to coat on both sides. Continue until all the meat is breaded.
Heat the butter and vegetable oil in a large skillet over medium to medium-high heat. Fry the steak strips 4 or 5 at a time, turning midway through. When golden brown, remove from the skillet to a paper towel-lined plate. Continue with the remaining meat. Cover loosely with foil to keep warm.
For the gravy: Pour off all the grease from the skillet, and then add 1/4 cup of the grease back in. Sprinkle on the flour. Whisk the mixture till it becomes a paste (add more flour if you need to) and cook the paste over medium-low heat until it's deep golden brown. Pour in about 3 cups of the milk, whisking constantly. Allow the gravy to cook and thicken, whisking regularly and adding more milk if it seems too thick right off the bat. Season the gravy with salt and pepper and pour into small dishes.