Melt 1 tablespoon tallow in the bottom of a large skillet (cast iron is my preference) over medium heat.
Once tallow is melted, add onions and mushrooms and sauté, stirring every few minutes for a total of 20 minutes or until onions are caramelized.
As the mushrooms and onions cook, butterfly steak by laying it flat on a cutting board, and using a sharp, thin knife to open up the steak. by cutting it crosswise so that when you are done it is twice as wide and half as thick. This makes a nice rectangle for you to roll up.
Once opened up, sprinkle beef evenly with red wine, garlic, sea salt, and pepper, and allow to rest.
When onions are golden, remove from heat and allow to cool slightly.
Top beef with arugula evenly, and then with onion/mushroom mixture.
Starting from the bottom (narrow end of the beef), tightly roll up the beef/arugula/onion layers.
Once rolled, turn so the seam side is down and the weight of the beef holds it together.
Wrap and tie kitchen twine 3-4 times around the beef roll firmly to hold it together.
Wipe out cast iron pan and melt the remaining 1 tablespoon tallow over medium-high heat.
Preheat oven to 375* F.
Sear beef roll on 3 sides for 2 minutes each once the skillet is hot again.
Turn to the 4th (unseared) side down and then cook in the oven for 30 minutes, or until an internal temperature reaches 130*
Remove from heat and cover with foil and allow to rest for 15 minutes before serving.