Blue Cheese Butter: Simply combine all ingredients together in a bowl and mix until combined and smooth with small blue cheese chunks. Chill in the refrigerator until it is ready to use.
Steak: Season the filet mignons on both sides with salt and pepper.
Add the oil to a large frying pan or cast-iron skillet over medium-high heat until it begins to lightly smoke.
Add the steak, turn the heat down to medium and then add in the garlic cloves, thyme and butter as well.
After 3 to 3 1/2 minutes flip the steak over and begin to baste them with the hot butter and oil from the pan. Cook for a further 3 to 3 ½ minutes to achieve a rare to medium-rare internal temperature.
Take the steaks out of the pan and let them rest on a plate for 5 minutes.
Mushrooms: Discard the thyme leaves and garlic cloves from the saute pan and turn the heat to high. Add in the mushrooms and saute for 3 to 4 minutes.
Once they begin to turn brown scoot them to the top of the pan and place the shallots, garlic, and butter on the other side of the pan where no mushrooms are at and quickly saute them until lightly browned, which takes about 1 minute.
Combine all of the ingredients and then deglaze with red wine and cook for 1 minute before adding in the beef stock.
Finish with salt and pepper.
Serve the filets with the mushrooms and blue cheese butter