Au Jus Burgers

This is a spin off of the classic roast beef au jus sandwich.   I came up with the idea a few years ago.  My family loves these burgers, especially the kids!

Au Jus Burgers
For each person I use 1/3 lb. of ground sirloin and form it into a patty (basically the 93% ground beef).  I grill these on the bbq on top of a cast iron pan.  Sprinkle garlic salt and onion salt on to taste while they cook.  Cook the burgers for 4-5 minutes per side.  Then spread just a small pat of butter on to each patty.  For the "buns" we use toasted french bread slices which have been very lightly buttered and sprinkled with Italian seasoning before being baked.  Sliced purple/red onions and swiss cheese are the only toppings we use and the au jus replaces any condiments.  The au jus dipping sauce is below.

Au Jus
In a small saucepan melt 1 stick of butter (you could probably use margarine if you prefer!?  I am a butter fan only, I don't use margarine in anything so I don't know how it will affect the au jus) over medium heat.
Add 3-4 small, sliced shallots  (the little purple skinned onions that are mildly flavored).
When the onions are translucent add 3 Tbsp. of flour and mix together.  Cook for 2-3 minutes, stirring constantly.
Next add 2 cans of beef broth and stir it into the rue.  Continue to cook over medium heat and stir until the broth thickens.  Remove from heat and cool slightly before serving.