Preheat the oven to 200 degrees F. Pat the cube steak thoroughly dry with paper towels. Then cut the steaks into strips approximately 1 to 1 1/2 inches wide and 3 to 4 inches long.
In a small bowl mix the flour, Cajun seasoning, and baking powder together. In another bowl, whisk together 3/4 cup milk, 3 eggs, and Worcestershire sauce. Place a large skillet over medium-high heat. Add enough oil to fill the skillet 1/4 inch deep.
Once the oil is between 350-375 degrees F, dip 6-8 steak strips in the flour mixture. Shake them off, then dunk the strips in the egg mixture. Shake off the drippings, then dunk back in the flour mixture. Shake off all excess flour. (Flour that falls off into the oil will burn and turn the oil dark.)
Gently place the strips in the hot oil and fry for 1-2 minutes per side. Use tongs to move the steak fingers to a paper towel lined plate. Add additional oil to the skillet if needed, and repeat with the remaining steak strips. Place the finished strips in the oven to keep warm.
Once all the steak fingers are fried, carefully wipe the skillet out with a paper towel. Place it back over medium heat and add the butter. Once melted, whisk in 1/4 cup of the remaining seasoned flour. Whisk until bubbling, then whisk in 2 cups of milk. Continue to whisk the gravy until it is thick. Taste, then season with salt and pepper as needed. Remove the gravy from heat. If the gravy starts to thicken too much, whisk in an additional 1/2 cup of milk.
Serve the steak fingers and warm country gravy together for dipping.