Prepare the steaks: Arrange the steaks in a dish; season with salt and pepper on both sides, sprinkle evenly with the liquid smoke and drizzle with the vegetable oil. Nestle the rosemary under the steaks and set aside at room temperature 2 hours, turning the steaks halfway through to infuse both sides with rosemary.
Make the rosemary butter: In a medium saucepan over medium-low heat, combine the butter and 1 teaspoon salt. Melt the butter, stirring to dissolve the salt, then add the garlic and rosemary. Continue cooking over low heat until the butter is fragrant, 10 to 12 minutes. Remove from the heat and discard the garlic and rosemary; set the butter aside.
Grill the steaks: Preheat a grill or grill pan to high. Remove the steaks from the dish, discard the rosemary and place the steaks on the grill. Cook about 5 minutes per side for medium rare. Remove from the grill, tent with foil and let rest 10 minutes before slicing.
Meanwhile, make the eggs: In a large bowl, vigorously whisk the eggs and add a splash of water (nothing more than a teaspoon). Melt the butter in a large nonstick pan over low heat but do not let it brown. Add the eggs and cook, whisking to release the cooked egg from the pan, until almost done but still wet, 5 to 6 minutes. Remove from the heat; add half of the cheese, a pinch of salt and a few grinds of pepper and continue whisking until done. Sprinkle the remaining cheese on top.
To serve, cut the steaks off the bone and slice against the grain; drizzle with the rosemary butter. Serve with the eggs.
Photograph by Con Poulos
Courtesy of Food Network Magazine
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