01 -
Pat dry the shrimp and steaks thoroughly. Immediately before cooking, season steaks with 1 teaspoon salt and 1/2 teaspoon black pepper. Season shrimp with 1/4 teaspoon salt and 1/4 teaspoon black pepper to taste.
02 -
Heat a large cast-iron skillet over medium-high heat until just smoking. Add vegetable oil and swirl to coat evenly. Place steaks into the skillet and sear for 4 minutes on the first side. Flip and sear for 3–4 minutes on the second side. Using tongs, sear all edges for 30–60 seconds each to render fat. Remove steaks when internal temperature is about 10°C below desired doneness. Place steaks on a plate, tent with foil, and allow to rest.
03 -
Reduce skillet heat to medium. Add butter, garlic quarters, and rosemary sprig. Once butter is melted, add seasoned shrimp in a single layer. Sauté shrimp for about 1 minute per side until pink, opaque, and cooked through. Remove skillet from heat.
04 -
Return steaks to the skillet, coating both steak and shrimp in the aromatic pan sauce. Spoon remaining flavored butter over to serve.