Season the steaks with salt and pepper. Heat the oil in a heavy skillet on medium-high heat. Add the steaks and sear on high heat until done to your preference, about 2-4 minutes per side for rare to medium rare.
Let the steaks rest in a heated oven until ready to eat.
Melt the butter in the same pan. Add the onion and saute at medium heat until tender, about 5 minutes. Add the garlic and thyme and saute until fragrant, about a minute.
Add the mushrooms and season with salt and pepper and saute until tender, about 5 minutes. Add the broth and cognac and deglaze the pan and simmer until it has thickened and reduced by about half.
Remove from heat and stir in the blue cheese and pour over the steaks. Garnish with additional blue cheese crumbles.