Heat 2 tablespoons oil in a large saute pan over medium-high heat until smoking. Sprinkle the steaks all over with salt and pepper. Put the steaks in the pan and cook, turning to brown all sides completely, until medium-rare, 8 to 10 minutes depending on how thick the steaks are. Remove the steaks to a platter with tongs and cover loosely with a tent of aluminum foil to keep the meat warm while you make the sauce.
Put the saute pan back over medium-high heat and add 1/4 cup olive oil. When the oil is smoking, add the mushrooms and cook, stirring, about 10 minutes, until golden brown. Then add the thyme and garlic, and season well with salt and pepper. Toss a few more times to cook the garlic, then dump the mushrooms out onto a platter. Take the pan off the heat, add the brandy, and cook until almost evaporated. Add the cream and cook that down 2 to 3 minutes until reduced by about one-half and thickened. Return the mushrooms to the pan with whatever juices have collected on the platter and simmer the whole thing another 2 minutes until thickened again. Season with salt and pepper.
Slice the steak thin against the grain. Taste the sauce for salt and pepper and serve.