Place each steak between two sheets of heavy plastic (or inside a resealable freezer bag) on a solid, level surface. Firmly pound each steak with the smooth side of a meat mallet to a thickness of 1/4-inch. Remove steaks from plastic.
Generously season each steak with salt and ground black pepper. Set aside.
Combine beef broth, barbeque sauce, hot sauce, and black pepper in a bowl. Add chilled butter to broth mixture but do not stir.
Heat oil in a large skillet over high heat until it just begins to smoke, about 1 minute. Place each steak in the pan; sear for 45 to 60 seconds on each side. Remove steaks from skillet and set them aside to rest.
Pour the broth mixture into the skillet and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Stir occasionally until butter is melted and incorporated, about 2 minutes.
Spoon broth and butter mixture over steak and serve.