Remove steaks from refrigeration 30 minutes prior to cooking and season generously with salt and pepper on all sides.
Heat olive oil and 1 tablespoon of butter in a cast-iron or heavy-bottomed skillet over medium-high heat until the butter is foaming and just beginning to brown.
Place steaks in the skillet and sear for 4 to 5 minutes per side for medium-rare (internal temperature of 130°F/54°C).
Remove steaks from the skillet and transfer to a warm plate; tent loosely with foil to rest for 5 to 10 minutes.
In the same skillet over medium heat, add the remaining 1 tablespoon of butter and the sliced mushrooms; sauté for 5 minutes until browned.
Add the minced shallots and garlic to the skillet, cooking for 1 to 2 minutes until fragrant and translucent.
Deglaze the pan with the red wine, using a wooden spoon to scrape the browned bits (fond) from the bottom; simmer until the liquid is reduced by half.
Stir in the beef stock and thyme, simmering for an additional 5 minutes until the sauce reaches a light syrup consistency.
Adjust the sauce seasoning with salt and pepper as needed, then pour the mushroom sauce over the rested steaks to serve.