First use a paper towel to dry off the pork tenderloin. Then, using a large sharp knife and a cutting board, remove any fat remaining on the pork. You may be able to pull it off with your hands. If not, cut it off with the knife.
Next remove the silverskin (connective tissue) on the tenderloin. You will need to poke the tip of the knife into the tenderloin just under one end of the silverskin, the gently and gradually move your knife back and forth as you slide it down underneath the sliverskin to remove it from the rest of the meat. It will need to be removed in multiple sections - if you try and remove it all at once you will cut away a large portion of the meat itself.
Once the silverskin is removed, measure out the kosher salt with a measuring spoon and sprinkle it all over the meat, spreading it around with your fingers until the meat is equally covered. Place the meat on a plate and in the fridge, uncovered, for 8 hours.
Take the tenderloin out of the fridge after the 8 hours is up and 30 minutes before you put it on the grill to let it come up in temperature.
Turn your grill on and let the temperature come up to about 375 degrees F. Just before it goes on the grill measure out the oil and pour it over the tenderloin, using your hands to cover the meat with the oil.
Once the grill has come to temperature, use a pair of tongs to place the meat on the grill. Close the lid and cook for 5 minutes, then open the lid and flip the tenderloin so the side that was up is now on the grill and being cooked. Close the lid and cook for an additional 5 minutes.
After the 5 minutes are up, check the temperature of the meat with a meat thermometer (we have used and loved our Thermapen for years - it's the purple one in the picture below). You want to pull the tenderloin off the grill at 140 degrees F. Cook the pork for an additional 3 to 8 minutes, depending on how thick it is and checking the temperature every couple of minutes as necessary.
When the thickest part of the pork reaches 140 degrees F, remove it from the grill and put it on a cutting board to rest for 5 to 10 minutes. Slice into medallions (roughly half an inch wide) to serve, sprinkling with chopped herbs if desired.