Preparing the Steak:

1. Trim the fat from the edges of the steak, leaving a layer 1/4-inch thick, then slash the layer of fat at 1-inch intervals.

2. In a small bowl, using the back of a spoon, mash together the garlic, anchovy paste, olive oil and pepper until smooth. Rub into both sides of the steak. Cover and let stand at room temperature for 1 hour.

Preparing the Sauce:

3. In a saucepan over medium-low heat, combine the potato and chicken broth. Bring to a simmer and cook, uncovered, until barely tender, about 10 minutes. Add the bell pepper and cook until heated through, another 3 minutes more. Drain, reserving the broth. There should be about 2 to 3 tablespoons.

4. In a food processor, with the motor running, drop the garlic cloves through the feed tub and process until chopped. Add the cherry pepper, pimiento pepper, potato-bell pepper mixture, thyme, vinegar and Tabasco. Process until smooth. With the motor running, slowly add the oil, 1 tablespoon at a time, and process until the mixture thickens. Transfer to a bowl and whisk in the reserved chicken broth. Season with salt and pepper. Cover and refrigerate until serving.

5. Prepare a hot fire in the grill. Position the grill rack 4 to 6 inches above the fire.

6. Place the steak on the rack and sear, turning once, until nicely browned, about 1-2 minutes on each side. Using long-handles tongs to hold the meat, sear the edges. Then grill over a medium-hot fire (move the steak to the edge of the fire or raise the grill rack), turning once, 16 to 20 minutes total for medium-rare, or until done to your liking. Transfer to a cutting board and cover loosely with aluminum foil. Allow to rest for at least 5 minutes.

7. Cut the meat from the bone, then slice the meat across the grain and serve. Pass the sauce at the table.