In a large sauce pan, heat the wine and sugar over medium-high heat. Bring to a boil and allow it to cook until reduced to about 1/3 cup. Remove from heat.
Meanwhile, melt one tablespoon of butter over medium heat in a non-stick skillet. Add the mushrooms and 1/2 teaspoon of salt. Cook, stirring occasionally, until browned, about 10 minutes. Add the fried onions and cook for a couple of more minutes. Remove mushrooms and onions to a clean bowl.
Season the steaks on both sides with the remaining teaspoon of salt. Add the remaining tablespoon of butter to the skillet. When melted, add the steaks and cook about 3 - 4 minutes per side. It may be necessary to increase the heat to medium-high to brown the steaks. They do not take long to cook, especially if you don't want them well-done.
Remove steaks to a clean plate and add the wine reduction to the pan. Scrape up all the browned bits from the bottom of the pan and immediately remove from the heat, or the wine will reduce too much.
Serve each filet burger topped with 1 oz. of Boursin cheese, a generous helping of the cooked mushrooms and onions and a drizzle of the red wine reduction.