Rub both sides of the beef filets with olive oil and season with salt and pepper.
Set beef filets aside and allow them to reach room temperature while preparing mushroom sauce.
Melt butter and 2 Tablespoons olive oil in a large skillet over medium high heat.
Add onions and cook for about 5 minutes.
Add mushrooms, garlic and thyme and cook for about 3 minutes more.
Stir in wine, scraping up any brown bits and cook until liquid is reduced by half, about 8-10 minutes.
Remove mushroom sauce to serving dish and keep warm.
The pan should still be hot from mushroom sauce.
The instructions below are for a medium-rare steak. Add 1-2 minutes to the cook time for a medium-well to well-done steak.
Add beef filets to pan and cook for about 3-4 minutes without moving the filets.
Flip the beef filets and cook for 3-4 minutes more.
Allow steak to rest for about 5 minutes before serving.
Top steaks with Burgundy Mushroom Sauce.