Preheat the oven to 400 degrees F.
Heat an oven proof skillet over medium high. Season the tenderloins well with salt and pepper (don't be shy with the pepper).
Add the olive oil to the skillet and heat. Add the butter and push it around to melt it and combine it with the olive oil.
Add the beef and sear it until it's browned on all sides. This should take about 8 minutes total.
Transfer the skillet to the oven and roast the meat to an internal temperature of about 125 degrees F for medium rare. This will take just under a half hour.
Transfer the tenderloins to a cutting board, tent with aluminum foil, and let them rest for 5 or 10 minutes.
Heat 2 tablespoons of the butter in a large skillet over medium high, then add the mushrooms and increase the temperature to high. Permit the mushrooms to cook undisturbed until they brown.
Shake the pan to turn them over, then add the next two tablespoons of butter along the sides of the pan.
Now continue to cook and stir until nicely browned, for about five minutes.
Add the shallots and cook for about two minutes, or until softened. Season with salt and pepper and add the thyme.
Take the skillet off the heat and add the wine. Return the pan to the heat and stir, scraping up the brown bits clinging to the bottom of the pan.
Add the heavy cream and bring to a boil. Remove from the heat.
Drizzle the mushroom ragout over the beef tenderloins and serve with goblets of a good hearty burgundy wine.