01 -
Use paper towels to thoroughly pat both the shrimp and steaks until completely dry. Right before you're ready to cook, sprinkle the steaks with 1 teaspoon of salt and ½ teaspoon of pepper. Season the shrimp separately with the remaining ¼ teaspoon salt and ¼ teaspoon pepper, adjusting to your preference.
02 -
Place a large cast-iron skillet over medium-high heat and let it get really hot—you'll know it's ready when it just begins to smoke slightly. Add the oil and swirl it around to coat the entire bottom of the pan evenly.
03 -
Carefully lay the steaks in the hot skillet and let them sear undisturbed for 4 minutes until a golden crust forms. Flip them over and cook for another 3 to 4 minutes on the second side. Use tongs to stand the steaks on their edges and render the fat cap, searing for 30 to 60 seconds per edge. Pull the steaks when your thermometer reads about 10 degrees below your target temperature—they'll continue cooking as they rest. Move them to a plate and loosely cover with foil.
04 -
Lower the heat to medium and immediately add the butter, garlic pieces, and rosemary sprig to the same pan. Let the butter melt and become fragrant with the herbs and garlic.
05 -
Arrange the seasoned shrimp in the aromatic butter in a single layer across the pan. Cook for approximately 1 minute on each side until they turn pink, opaque, and fully cooked. Turn off the heat right away to prevent overcooking.
06 -
Place the rested steaks back into the pan and turn them to coat in the herb butter. Spoon the flavorful pan sauce generously over both the steak and shrimp. Serve immediately with extra butter sauce drizzled on top.