Place the flour, salt and pepper in a large mixing bowl. In another bowl, whisk 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 4 hours, or up to 24 hours.
Transfer dough to a floured surface and roll out to 3/16-inch thickness, approximately a 24 by 18-inch rectangle. Trim away extra dough, if necessary. Sprinkle the remaining herbs on the center section of the dough and gently press down.
Preheat oven to 400 degrees F.
In order to achieve uniform cooking, fold over slender tail end of tenderloin and tie with kitchen twine. Set a large electric griddle at its highest setting; brush the tenderloin with the olive oil and sear on all sides until well browned, approximately 10 minutes. Rest the meat for at least 5 minutes or until it is cool to the touch so as not to melt the dough.
Place the tenderloin in the center of the dough. Fold top part of dough over, flipping back about 1-inch of dough onto itself. Repeat with the bottom half of the dough. Press together the 2 flaps of dough and seal. Make sure the dough is not too tight around the tenderloin. At the ends of the tenderloin, press together dough to form a seal and cut away any excess. Transfer to a sheet pan, place in the oven and roast to an internal temperature of 125 degrees F, approximately 25 to 30 minutes. Remove from the oven and allow to rest for 30 minutes or up to 1 hour. The tenderloin will continue to cook 10 to 15 degrees more. Cut salt crust at 1 end and extract meat by pulling out of dough tube. Slice and serve immediately.