This is a simple recipe that makes everyone hungry. It's a good feeling to make your own onion rings and watch as people crunch down on them as they cut into this tasty steak. I serve the meat with a little vinegar so the onion rings get a salt and vinegar vibe when you eat the two parts of the dish together. This is not the type of dish that can be made in advance and held, so get everything ready and cook the meat and onion rings when you are ready to eat!
Prepare the batter: Pour the beer into a medium bowl and stir in the vodka and sparkling water. Slowly whisk in the baking soda, paprika and 1 1/2 cups of the flour. The batter should be fairly thick but also easy to stir. If it's a little loose, whisk in the remaining 3/4 cup flour, 1/4 cup at a time. If it's too thick, add a splash of water. Do not overmix. Set aside in a warm place for at least 15 minutes.
Get ready to fry: Pour the oil into a heavy-bottomed pot. Heat the oil slowly to 375 degrees F. Use a thermometer to monitor the temperature. Line a baking sheet with a kitchen towel to drain the onion rings once they are cooked.
Cook the steak: Heat a large cast-iron skillet over high heat. Add the oil. When it begins to smoke lightly, season the steak with salt and use a pair of metal tongs to gingerly place the steak in the hot oil. Cook, 4 to 5 minutes, on each side.
Doneness: If using a meat thermometer, rare registers between 125 and 130 degrees F. For medium rare, 130 to 135 degrees F; and between 135 and 140 degrees F for medium. If you like your steak a little more cooked, leave it in the pan a few minutes longer on each side. Let it rest on a flat surface and cover with foil to keep warm while you make the onion rings.
Fry the onion rings: Test the batter and the temperature of the oil at the same time by dipping an onion round into the batter, gently shaking off the excess batter and carefully plunging it into the oil. Fry until crispy, 1 to 2 minutes, and remove it from the oil carefully with a slotted spoon. Fry the onion rounds in small batches, draining them on the kitchen towel-lined baking sheet. Salt immediately.
Serve: Slice the steak into 1/2-inch-thick pieces, season with salt and drizzle with the balsamic vinegar. Arrange on a serving platter with all the cooking juices and serve with the onion rings in a bowl on the side.