Preheat an outdoor grill for medium-high heat. Melt butter in a large skillet over medium-high heat.
Sautee the shallot until transparent, then add mushrooms, and cook, covered, until darkened, about 5 minutes.
Remove mushrooms from pan, and set aside. Deglaze the pan with one can of beef broth, and burgundy wine. Increase heat, and bring to a boil. Allow the mixture to boil until it has reduced by 1/
Grill the sirloin tips to desired doneness. Season with salt and pepper if desired.
Remove to a plate, and set aside.
When the sauce is reduced, stir in the other can of beef broth, and garlic. Return to a boil, and continue to cook for another 5 to 10 minutes. Sauce will be thin like au jus.
Whisk in flour, and cook until the sauce is the desired thickness. Taste and adjust seasoning if necessary. Stir in the mushrooms.
