Step 1

Prepare a grill for high indirect heat (for a charcoal grill, bank coals on one side of grill; for a gas grill, leave one or two burners off); oil grate with vegetable oil. Coarsely chop 2 Tbsp. peppercorns, then coarsely chop basil and mint right on top of peppercorns. Transfer to a small bowl and mix in olive oil; season with salt. Coarsely chop a few more peppercorns and set aside for serving.

Step 2

Season steak generously with salt. Grill over direct heat, keeping tenderloin (the smaller side) away from the most intense heat and turning steak about every minute or so to control flare-ups and ensure even browning, until deeply browned on all sides (including standing it on its side with tongs to render and brown fat around edges), 6–8 minutes.

Step 3

Move steak over indirect heat (still positioning tenderloin side away from the heat) and grill, turning every 1–2 minutes and moving closer to or farther away from heat as needed to build even color, until an instant-read thermometer inserted into the thickest part of steak registers 120° for medium-rare, 10–12 minutes. Transfer to a wire rack set over a rimmed baking sheet and let rest 15–30 minutes.

Step 4

Transfer to a cutting board and cut meat away from each side of the bone, then slice crosswise. Serve topped with sauce and reserved peppercorns.