How To Make Steak Sandwich With A Kick

My long time martial arts instructor and friend opened his own school so I have resumed training as of this morning. It did not occur to me that he must have learned training techniques from Marquis de Sade until I was doing push ups up and down the length of the floor. You'd do a push up and then while in the up position, move one spot to the side, then do another push up, repeat.
By the time I got home, my appetite was as voracious as a locust that had smoking pot. I stuck my head in the fridge and saw that leftover small roast from the strip loin that I had broken down into steaks. Better yet it hadn't finished thawing, perfect for making a steak sandwich! A steak sandwich with a kick.
Steak Sandwich With A Kick
Serves 4
1 Tbsp butter
1 Tbsp beef tallow or other oil
2 yellow onions, peeled and sliced thin
2 Tbsp butter
2 Tbsp all purpose flour
1 cup half and half
1 cup Three Alarm Colby Jack cheese, shredded (or other spicy cheese)
2 Tbsp beef tallow or other oil
4 hoagie rolls
2 lb strip or ribeye roast
Salt and pepper to taste
Over low heat, melt the butter and tallow. Add the sliced onions, season with a little salt and caramelize them for 1 hour.
About 20 minutes before the onions are done, make the cheese sauce. In a small sauce pan, melt butter and whisk in the flour. Keep stirring for a few minutes until you get a blond roux. It will be a dryish paste and have a nutty aroma. Whisk in the half and half, making sure the roux dissolves evenly. Let simmer for 5 minutes and then add the cheese in small batches.
The secret to good steak sandwiches is to cut your meat thin and then pound it thinner. Slice the beef into 1/4" or thinner slices. A meat slicer helps but these were done by hand (my Waring Pro meat slicer died after 2 years). It helps to have the meat partially frozen when slicing but make sure they finish thawing when you start to beat them.

Get a cast iron pan preheated over medium high heat and add the beef fat or oil.  I was using beef fat because 1) I rendered it and saved it from the scraps last week and 2) it has a high smoke point.  

Season the steaks with salt and pepper and then pound them thin with the serrated side of a meat mallet.  Place them into the hot pan.  Work in small batches to avoid overcrowding the pan.  After about 30 seconds, start tearing them apart and toss like stir fry with a pair of metal spatulas.   It should only take about 3 minutes to cook each batch of beef.