Steps:
- For the maître d' butter: Put the butter, parsley and lemon zest and juice in a large bowl. Mix with an electric hand mixer until all of the ingredients are incorporated and the butter is smooth. Season to taste with kosher salt.
- For the court bouillon: Set up a large pot of boiling water and season liberally with kosher salt. It should be as salty as the sea. Add the white wine, coriander seeds, black peppercorns, celery, garlic, onions, thyme and bay leaves. Squeeze the lemon into the water, add to the pot and simmer for 10 to 12 minutes.
- For the lobster: Add the lobster to the court bouillon, cover the pot and cook for 10 minutes. Transfer the lobster to a sheet tray to cool. Remove the claws and knuckles and take the meat out of the shells. Slice the lobster in half lengthwise through the body and the tail. Remove any roe from the cavity.
- Heat a small saute pan over medium-high heat with the olive oil. Add the shallots, sprinkle with kosher salt and cook, stirring occasionally, until the shallots are translucent, 3 to 4 minutes. Add the halved lobster bodies, flesh-side down, and sear for 2 minutes. Remove the lobster, then spread the inside with some of the maître d' butter. Add the claw and knuckle meat into the pan, sprinkle with kosher salt and cook for 1 to 2 minutes. Toss in the chives and stir to combine, then turn off the heat.
- For the steak: Preheat the oven to 400 degrees F. Heat the canola oil in a large cast-iron pan over medium-high heat. Season the steak on all sides liberally with kosher salt and black pepper. Place each steak upright on its fat-cap side onto the pan and nestle the steaks next to each other so they stand up. Cook until the fat renders down, 5 minutes. Turn the steak onto one of the flat sides and sear until a crust forms, about 4 minutes, then flip the steak and continue to cook until a crust forms, another 4 minutes. Add the butter, garlic, rosemary and thyme to the pan. Tilt the pan and baste the steak with the butter and aromatics. Transfer the steaks to a sheet tray lined with a rack. Spoon some of the leftover butter and aromatics over the steak. Transfer to the oven and cook for 10 minutes or until a thermometer inserted into the center registers 130 degrees F for medium rare. Transfer the steaks to a cutting board and let rest for 5 to 10 minutes. Slice the steak against the grain.
- For the potatoes: Bring a medium saucepan of water to a boil and season generously with kosher salt. Add the black peppercorns, garlic and thyme. Reduce the heat and simmer for 10 minutes. Add the potatoes and cook until fork tender, 15 minutes. Drain the potatoes and let them cool. Smash the cooled potatoes lightly with the palm of your hand until flattened. Heat the duck fat in a nonstick pan over medium-high heat. Add the potatoes in a single layer, add the rosemary, then reduce the heat to medium and cook until golden brown and crispy, flipping halfway through, 5 to 7 minutes. Season to taste with kosher salt.
- To serve: Fill the lobster halves with the claw and knuckle meat and plate alongside the sliced steak and crispy duck fat potatoes. Serve with additional maître d'butter if desired.
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