Let the rib eye come to room temperature. Rub it with the vegetable oil on both sides.
Heat a heavy skillet over a high heat on the stove. Once hot, add the steak and cook, turning often, until rare (3 to 4 minutes, total). Remove from the skillet to a cutting board and let rest for 10 minutes. Very thinly slice the steak.
Mix the steak with paprika, salt, pepper and cornstarch in a small bowl.
Cut the top and base off of the onions, peel away the dry papery skin. Cut the onion into 1 1/2 inch thick rounds. Pop out the layers to get onion rings – you’ll need 4 large onion rings for this recipe. Save the remaining onion bits for another recipe.
Place the 4 onion rings on a large plate or a cookie sheet lined with parchment paper.
Take 1/4 of the steak and place on a square of provolone cheese. Push the whole thing into the onion ring to fill it. Repeat with the rest of the steak and cheese slices.
Freeze the onion rings for at least 2 hours, until solid.
Place the flour in a shallow bowl. Crack the eggs into a second shallow bowl and beat with a fork. Place the panko into a third shallow bowl.
Take each frozen filled onion rings and carefully coat entirely with the flour, then the egg then the breadcrumbs. Once coated, dip each onion ring into the egg again and the breadcrumbs again. Set aside.
Fill a medium pot with 2-inches of vegetable oil and place over a medium heat and let the oil come to 350 degrees F (measure this with a kitchen thermometer). Once the oil is at the right temperature, gently lower in one of the onion rings. Let it cool until golden all over, turning occasionally to ensure even browning. Remove with a slotted spoon to a plate lined with paper towel to allow the excess oil to drain. Repeat the frying with the other onion rings.
Serve the onions rings hot with the marinara sauce, for dipping.