Pat dry shrimp and steaks thoroughly with a paper towel. Just before cooking, season the steak season with 1 tsp salt and 1/2 tsp black pepper, and season shrimp with 1/4 tsp salt and 1/4 tsp black pepper or to taste.
Heat a large cast-iron skillet over medium/high heat. Once it’s hot to the point where it’s just starting to smoke, add 1/2 Tbsp olive and swirl the skillet to coat.
Add the steaks and sear for 4 minutes on the first side then flip and sear for 3-4 minutes on the second side. Using tongs, turn the steaks on their sides to render the white fat and sear the edges (30-60 seconds per edge). Remove from the skillet when it is about 10 degrees from your desired doneness on a thermometer (the temperature will continue to rise as it rests). Transfer the steaks to a plate and tent with foil to rest.
Reduce the heat to medium and right away add 3 Tbsp butter, quartered garlic cloves, and a sprig of rosemary.
Add the seasoned shrimp to the pan and spread in a single layer. Sauté about 1 minute per side or until pink and opaque and cooked through then immediately remove the skillet from the heatReturn steaks to the pan and turn to coat in pan sauce, spooning more of the flavored butter over the steak and shrimp. Serve drizzled with more pan sauce.
Recipe Notes
Steak Final Doneness Temperatures: Remove the steaks about 10 degrees before they reach your desired doneness temperature on a thermometer. I remove my steaks at 125˚F to reach a final resting temperature of 135˚F for medium doneness.
130˚F Medium Rare
135˚F Medium
140˚F Medium-Well
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