How to Make It
Squeeze as much liquid from the potatoes as possible. Put the potatoes in a large bowl and stir in the chives and parsley; season with salt and pepper.
In a large nonstick skillet, melt 4 tablespoons of the butter in the oil. Stir in the potatoes and spread in an even layer. Cook over moderate heat, turning once, until the potato cake is golden and crisp, 35 minutes; keep warm.
Preheat the oven to 400°. Season the meat with salt and pepper. In a large ovenproof skillet, sear the meat over high heat, turning once, until well browned, about 8 minutes. Transfer the skillet to the oven and roast the meat for 15 minutes for medium rare. Transfer the steaks to a plate.
Set the skillet over high heat. Add the demiglace and thyme and cook, stirring, until reduced to 1/4 cup. Swirl in the remaining 2 tablespoons of butter and season with salt and pepper.
Cut the potato cake into 4 wedges and transfer to warmed plates. Set the steaks on the wedges. Drizzle the sauce around the steaks and serve at once.