Cheese-Steak Sandwiches on the cheap

This is probably one of my favorites... and I don't eat it often.  And, honestly, I've never made one at home until now.
When I was shopping several weeks ago, I found a pack of thin sliced boneless chuck that weighed 12 oz marked down to $1.68.  I froze it in 4 oz portions.  The first thing that ran through my mind was "cheese-steaks"!
I added a 69¢ cent package of mushrooms from Aldi's and a 17¢ onion (also from a bag of onions from Aldi's), some whole wheat hot dog rolls from Aldi's, and cheese sauce...I used cheese sauce to stretch one of the most expensive ingredients in this dish... cheese... to get creamy goodness and use less cheese. I was really pleased with the result. While I will admit, they were NOT as tasty as the cheese-steaks from my local sub shop, they cost me substantially less.  I made six of these for around $4.... and one cheese steak would easily cost me $8 around the corner.  

Here is how you can make 6 small cheese-steak subs at  67¢ each (round up to 70¢ to account for price of flour).

8 oz of boneless chuck, sliced really thin in slivers (Giant, marked down, $1.12)
1 package mushrooms, sliced (Aldi's, 69¢)
1 onion, sliced (Aldi's, 17¢)
1 cup milk (Target, organic milk with coupon 31¢)
2 T flour ?
3/4 cup shredded cheddar cheese.  (Target, sale, 75¢)
6 whole wheat hot dog rolls (Aldi's, 98¢)

In a pan, sautee onion and mushrooms until onions are translucent, and all liquid has cooked off of mushrooms.
Add boneless chuck to pan
Season with salt and pepper, or your favorite seasoning.
Cook until meat is cooked through.

Meanwhile, mix 2 tablespoons of flour into 1 cup of milk.  Pour into saucepan, stirring frequently, heat until milk thickens.  Stir in cheese, and stir until cheese is melted.  Remove from heat.

Spoon meat/onion/mushroom mixture evenly between six rolls, spoon cheese sauce evenly over meat. If you wish, sprinkle a small amount of shredded cheese on top as a garnish.  Serve while hot.