Combine the flour, salt, and pepper in a large mixing bowl. In another bowl, whisk together the egg whites and water and add to the dry ingredients along with 2 tablespoons of the herbs. Combine with a potato masher until the mixture begins to come together, then knead with your hands for 1 to 2 minutes. Transfer the mixture to a large zip-top bag, seal, and let stand at room temperature for at least 2 hours or up to 24 hours.
When ready to roast, heat the oven to 400ºF.
In order to achieve uniform cooking, fold over the slender tail end of tenderloin and tie with kitchen twine. Set a large electric griddle to its highest setting. Brush the tenderloin with the olive oil and sear on all sides until well browned, about 10 minutes. Rest the meat until it is cool to the touch so as not to melt the dough, at least 10 minutes.
Transfer the dough to a floured surface and roll out to 1/4-inch thick, approximately a 24-by-18-inch rectangle. Trim away extra dough and brush away any excess flour, if necessary. Sprinkle the remaining herbs on the center section of the dough and gently press down.
Place the tenderloin in the center of the dough. Fold the top part of dough over, flipping about 1 inch of dough back onto itself. Repeat with the bottom half of the dough. Press the 2 flaps of dough together and seal, making sure the dough is not too tightDoing so will only hold moisture right up against the meat causing it to stew. around the tenderloin. At the ends of the tenderloin, press dough together to form a seal and cut away any excess. Transfer to a half sheet pan, place in the oven, and roast to an internal temperature of 125ºF, 25 to 30 minutes.
Remove from the oven and allow to rest for 30 minutes to 1 hour. The tenderloin will continue to cook 10 to 15 degrees more. Cut away the salt crust at one end and remove the tenderloin from the dough tube using tongs. Slice and serve immediately.