Remove the picanha from the fridge at least 1 hour before cooking to bring it to room temperature. Preheat the oven to 350°F.
Using a sharp knife, score the fat cap of the picanha in a crosshatch pattern without cutting into the meat.
Generously rub coarse salt and freshly ground black pepper all over the roast.
Place the picanha fat-side up on a rimmed baking sheet (use a wire rack if you have one) and drizzle with extra-virgin olive oil.
Roast for 45–50 minutes for medium doneness (pink inside). If you prefer it more well done, roast for another 10–15 minutes until the fat is golden and crispy.
Remove the picanha from the oven and transfer it to a cutting board. Loosely tent with aluminum foil and let it rest for 10–15 minutes.
Slice the picanha into thick slices against the grain. Serve with roasted potatoes, a simple green salad, or grilled vegetables.