Take the picanha out of the refrigerator 30 minutes before cooking. Pat it dry. With a sharp knife, score the fat cap in a shallow crosshatch, cutting through the fat but not into the meat.
Cut the picanha with the grain into 3 or 4 thick steaks, each about 2 inches wide. Bend each piece into a C shape with the fat on the outside and thread it onto a long metal skewer. If you are not using skewers, leave them as thick steaks.
Rub the coarse salt all over the meat and fat, pressing it in. Add pepper if you like, although the classic version uses salt only.
Prepare a charcoal or gas grill for medium-high heat with a cooler zone. Grill the skewers fat side down first until the fat is golden and crisp, about 8 minutes, moving them to the cooler zone if flare-ups get too strong.
Turn and grill the meat sides for 15 to 20 minutes more, turning every few minutes, until the thickest part reaches 125 to 130°F (52 to 54°C) for medium-rare.
Rest the meat for 5 minutes. Tap off any excess salt, then carve thin slices against the grain, just as the passadores do at a churrascaria. Melt the butter with the garlic and brush it over the slices if you like.