Preheat the oven to 250 degrees F. Bring a large cast-iron grill pan to medium-high heat.
Pat the steak dry and sprinkle liberally with salt and pepper. Drizzle with oil. Place the steak into the pan and sear until browned (without moving the steak), 3 to 4 minutes. Turn the steak over and cook a further 3 to 4 minutes on the second side for medium-rare. Remove the steak from the pan and add to a cast-iron pan. Put the steak into the oven for 5 minutes to finish cooking through. Remove from the oven and set aside to rest on a plate while you prepare the sauce.
Place the cast-iron pan over medium heat and add the oil to heat. Once heated, add the shallots to the pan. Saute until translucent, 3 to 4 minutes. Add the thyme leaves, and then remove the pan from flame (for safety purposes) and add the brandy. Ignite the brandy by returning to the stove top and tilting the pan toward the open flame, or carefully lighting with a lighter or match. Once the flames subside, add the cream and swirl to incorporate. Add the peppercorns and simmer the sauce until it has reduced by two-thirds to a smooth, slightly thick consistency, 3 to 5 minutes. Add any pan drippings to the sauce. Season with salt, if needed. To finish, remove the pan from the heat and swirl in the butter.
To serve, slice the rested hanger steak into 1/2-inch strips, against the grain, and serve with a drizzle of brandied green peppercorn sauce over the top.