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Heat a medium stainless steel or cast-iron skillet over medium-high heat. Pat steak dry; season all over with 1 tsp. kosher salt.
In a small bowl, mix butter, garlic, lemon zest, chives, mustard, hot sauce, horseradish, pepper, paprika, chili powder, and remaining ¾ tsp. kosher salt until smooth.
Pour oil into skillet and swirl to coat. Place steak in pan and cook, undisturbed, until a golden brown crust forms and steak easily lifts from pan, 3 to 4 minutes. Turn steak and reduce heat to medium. Add 2 Tbsp. cowboy butter to pan and let melt. Using a large spoon and tipping skillet if needed, scoop up some melted butter and spoon it over steak. Cook until instant-read thermometer inserted into the center registers 125°, 3 to 4 minutes more.
Transfer steak to a cutting board and let rest 5 minutes. Cut away from bone and slice across the grain. Top with sea salt, a dollop of cowboy butter, and a sprinkle of chives.