Pat the pork dry with a paper towel then remove the fat and silverskin of the pork with a large sharp knife. Measure out the kosher salt with a measuring spoon and sprinkle it over the pork. Spread it around with your hands until the pork is covered with the salt, then place the tenderloin on a plate and in the fridge, uncovered, for 8 hours.
Remove the pork from the fridge 30 minutes before you grill it. While the pork is sitting out, cut the peaches into eight pieces. First slice it in half all the way around with a large sharp knife. Remove the pit by using the tip of the knife to loosen it, then remove it with your fingers.
Cut each peach half into two pieces, then cut those pieces in half again, resulting in eight pieces of peach. Repeat the process with the second peach. Pour half a tablespoon of oil over the peach slices and rub the oil over each slice with your fingers. Make sure each slice is well covered so it doesn't stick to the grill. Pour the remaining tablespoon of oil over the pork and rub it all over with your hands, making sure it's fully covered.
Light the grill and bring the heat up to 375 degrees F. Use a pair of tongs to place the pork on the grill. Close the lid and cook it for 5 minutes, then use the tongs to flip the pork to the other side (so the side that was up is now on the grill and being cooked). Close the lid again and cook for another 5 minutes.
After the second 5 minutes, use a meat thermometer to check the temperature of the pork (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 pork has come to temperature, pull it off the grill and onto a cutting board and let it rest for 5 to 10 minutes. While the pork is resting, grill the peaches. Use a pair of tongs to place the peach slices on the grill. Close the lid and cook for 2 minutes, then open the lid and flip the peaches onto the uncooked side. Close the lid again and grill for another 2 minutes, then remove the peach slices from the grill. Set aside.
Using a large knife, slice the pork into medallions (roughly half an inch wide). Put the lettuce on a large platter and place the sliced pork and peaches on it. Drizzle aged balsamic vinegar over everything and serve immediately.