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Prepare grill for medium-high heat; lightly oil grill grate. Mix butter, 1 teaspoon pepper, and 1/2 teaspoons kosher salt in a small bowl; set aside.
Season steak with kosher salt and pepper. Grill, turning occasionally, 7–10 minutes for medium-rare. Let rest 5 minutes, then top with pepper butter.
Meanwhile, combine radishes and remaining 1 tablespoon oil in a medium bowl; season with kosher salt and pepper and toss to coat. Grill radishes until crisp-tender, about 2 minutes per side.
Season steak with sea salt, slice, and serve with radishes and lemon wedges.
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