For the steak: Preheat a convection oven to 400 degrees F.
Mix together the salt and brown sugar and the porcini, chile de arbol and garlic powders in a bowl, using your fingers to make sure all the ingredients are evenly distributed. Rub the steak generously on all sides with the spice rub. Wrap tightly in plastic wrap and leave to sit at room temperature for 20 minutes.
Preheat a cast-iron pan over high heat. When the pan is hot, add enough olive oil to coat the bottom. Unwrap the steak and add it to the pan; cook until well charred on all sides. Remove the steak to a baking sheet, transfer to the oven and roast until medium-rare, about 6 minutes. Allow the steak to rest for 4 to 5 minutes, then cut the steak off the bone and slice it across the grain, on the bias.
For the chili lobster: Bring a large pot of water to a boil. Add the coriander, celery, halved garlic head, lemon, thyme, white wine and a good amount of salt.
Add the lobster and poach for 6 minutes. Remove the lobster to a baking sheet to cool.
In a large saute pan, add enough oil to coat the bottom. Add the 5 garlic cloves, chili paste and some salt and cook over medium heat until the garlic turns golden brown and the mixture fragrant.
Pull the claws off the lobster and set aside. Set the body upside down on a cutting board and slice the entire lobster in half lengthwise. Discard the contents inside the head and body cavities, leaving the tail meat intact. Remove the meat from the claws and add it to the garlic-chili sauce; cook just until the meat is warmed through. Remove the meat from the pan and set aside. Place the lobster halves cut-side down in the sauce and sear for 1 to 2 minutes. Remove the lobster to a plate. With the pan off the heat, stir in the parsley.
In a small bowl mix together the arugula, red onion and a tablespoon of the garlic-chili sauce from the pan. Season with salt and toss to coat.
Assembly: Place some of the arugula reserved for garnish on one side of a serving platter and lay the sliced steak over it. Pour any meat juices from the baking sheet over the steak. Arrange the lobster halves on the other side of the platter and fill the cavities with some of the arugula salad. Top with the warmed claw meat and pour a couple tablespoons of the garlic-chili sauce over the lobster.
Drizzle both steak and lobster with big fat finishing oil (extra-virgin olive oil).
Recipe courtesy of Anne Burrell