Preheat oven to 250°F. Sprinkle steak with salt and 1 teaspoon of the pepper. Place steak on a wire rack set inside a rimmed baking sheet. Bake in preheated oven until a thermometer inserted in thickest portion of meat registers 115°F for medium-rare (the steak will cook more when it is finished in the skillet), about 35 minutes.
Meanwhile, place butter, shallot, thyme, and remaining 4 teaspoons pepper in a small bowl; fold mixture together using a spatula until thoroughly combined. Cover and chill the compound butter for about 30 minutes, or store in an airtight container in refrigerator for up to 1 week.
Heat oil in a 12-inch cast-iron skillet over high until oil shimmers and just begins to smoke. Add steak; cook until golden brown, 1 minute per side. Transfer steak to a cutting board.
Remove skillet from heat, add wine to skillet, and let mixture reduce, stirring constantly, until reduced by half, about 15 seconds. Add broth. Return skillet to heat over medium-high and bring to a simmer. Simmer, stirring constantly, until reduced by half, about 2 minutes. Remove from heat. Add 2 tablespoons compound butter and whisk until butter has melted and sauce emulsifies. Season with additional salt to taste.
Slice steak into 1/4-inch-thick pieces and divide between two plates. Spoon pan sauce over steak and serve.
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