Step 1: Arrange the cotton cloth on a work surface on the diagonal (like a diamond), so that one corner points down toward you. Spread the salt out on top of the cloth to form a layer ¼ inch thick that extends to within 1 inch of the bottom edges of the cloth. Sprinkle the oregano evenly over the salt.
Step 2: Arrange the beef tenderloin crosswise on top of the salt about 4 inches up from the point of the cloth closest to you; the tenderloin should be parallel to your shoulders. Starting at the corner closest to you, roll the tenderloin up in the cloth and salt. The idea is to make a compact roll. Now take the points of cloth at each end of the resulting cylinder and tie them together on top of the tenderloin. Tuck in any loose ends. The goal is to form a tight cylinder. (If necessary, tie the center of the cylinder with butcher’s string to secure it.) You should roll up the tenderloin just prior to grilling.
Step 3: To grill: If you are using a charcoal grill, light the coals in a chimney starter and rake them out in an even layer at the bottom of the grill. You will not need a grill grate. Place the wrapped tenderloin right on the coals, knotted side up, and grill it for about 9 minutes. Using long-handled tongs, gently turn the tenderloin package over and grill it for about 8 minutes longer. Do not be alarmed if the cloth burns; it’s meant to. In fact, the whole package should look about as appetizing as a fire-charred log.
If you are using a gas grill, preheat it as hot as it will go; you need a “2 Mississippi” fire. There is no need to oil the grill grate. Place the wrapped tenderloin on the hot grate, knotted side up, and grill it for about 9 minutes. Using long-handled tongs, gently turn the tenderloin package over and grill it for about 8 minutes longer. You may need a little more cooking time and the crust won’t burn as black when charcoal grilled but the tenderloin will still turn out pretty tasty.
Step 4: Use an instant-read meat thermometer to test the tenderloin for doneness, inserting it through the cloth into the center of the meat. When cooked to rare, the internal temperature will be about 125°F; to medium-rare, 140° to 145°F.
Step 5: Transfer the charred tenderloin to a metal platter or rimmed sheet pan and let it rest for 2 minutes. Lift the tenderloin with tongs and tap it hard with the back of a large, heavy chef’s knife (you may need to tap it several times). The burnt shell should crack and come off. Using a pastry brush, brush any excess salt off the tenderloin. Transfer the tenderloin to a clean platter, cut it into 2 to 4 pieces and serve at once.