Grilled Porterhouse with Brown Butter and Horseradish

• 1 porterhouse steak (2 inches thick; 2 pounds), at room temperature
• Kosher salt and freshly ground pepper
• Vegetable oil, for grill
• 4 tablespoons unsalted butter
• 3 cloves garlic, smashed and peeled
• 1 cup packed arugula
• 1 cup sliced celery, plus 1/4 cup leaves
• 1/4 cup pitted, sliced green olives, such as Castelvetrano
• 1 tablespoon fresh lemon juice
• Fresh peeled horseradish, for serving

• Step 1

  Prepare grill for direct- and indirect-heat cooking. Pat steak dry and season generously with salt and pepper; let stand 10 minutes. Brush grates with oil and grill steak over high direct heat, turning occasionally, until a nice crust forms, 6 to 8 minutes a side.

• Step 2

  Transfer to indirect heat, cover, and continue to cook, flipping once more, until a thermometer inserted into thickest part (nearest but not touching bone) registers 125°F for medium rare, 8 to 10 minutes more.

• Step 3

  Meanwhile, combine butter and garlic in a saucepan. Cook over medium-high heat (you can do this on the direct-heat side of the grill), swirling occasionally, until butter turns golden brown and gives off a nutty aroma, about 5 minutes. Remove from heat.

• Step 4

  In a bowl, toss arugula, celery and leaves, and olives with lemon juice. Slice steak from bone, then carve against the grain into thick slices. Pile salad on top of steak; drizzle brown butter generously over both. Grate horseradish over top; serve.