Prepare steak rub: Add salt, pepper, paprika, and garlic powder to a small bowl and mix. Rub both sides of the steak generously with the seasoning. Let sit for 30 minutes to maximize flavor. Prep lobster tails while waiting
In a separate small bowl, melt the butter. Add worchestire, crushed garlic, and lemon juice. Whisk to combine.
Preheat the broiler for the lobster.
Heat a cast iron grill over high heat. Once hot, place both pieces of steak onto the grill. Cook for 3 minutes. Flip, and add the butter mixture to the pan on top of each steak. Top with 2 sprigs of thyme per steak. Cook for 3 minutes. Lower heat and cover. Cook steak to desired temperature. Check temperature before removing from heat, look for the temp to be 5 °F (-15 °C) less than desired as it will raise about 5 °F (-15 °C) as it rests. Rare will be done fairly quickly and will only need to cook an additional 1-2 minutes, reaching 115 °F (46 °C) before removing. Medium rare will take an additional 2-4 minutes, reaching 130 °F (54 °C) before removing. Medium will take 4-5 minutes, reaching 140 °F (60 °C) before removing. And medium well will take 5-6 minutes, or 145 °F (63 °C) before removing.
Note: times above are for a 1” thick steak. Because the cut and thickness may vary, the best practice is to sear both sides of the meat as instructed, cover, and use a meat thermometer to check desired temp.
Let the steak rest for 5 minutes.
For the lobster:
Cut a rectangle down the top of the lobster tail shell and discard. Gently pull the lobster meat away from the sides and above the rectangle. Place onto a foil lined cookie sheet or into an oven safe pan.
Roughly chop shallot. Add to a food processor with garlic cloves, chopped basil, lemon juice, salt, black pepper, paprika, and garlic powder. Melt 3 tbsp butter and add to the food processor. Pulse for 15-20 seconds.
Top each lobster with 1 tablespoon (14g) of shallot butter paste. Place leftover paste into a saucepan with 2 tablespoons (28g) butter over low heat until melted. Set aside.
Place lobster under the broiler for 6 minutes.
Remove from the oven and pour 1 teaspoon of melted butter mixture onto the top. Serve with remaining butter as dip.
Plate lobster tails and steak with your favorite vegetables. Enjoy!