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.