In a food processor, combine basil, walnuts, garlic, salt and pepper. Process for several minutes until blended. Add in parmesan and olive oil and blend until desired consistency.
Preheat oven to 450 degrees F. (or use a grill)
Bake tenderloins on baking sheet and cook for about 10 minutes. Spread half of the pesto over the tops and return to the oven for an additional 7-10 minutes, until internal temperature of pork reaches 145 degrees. Oven temps may vary, so using a meat thermometer yields best results!
Remove from oven and allow to rest about 10 minutes before slicing.
Serve with remaining pesto and enjoy!
Notes
Trim the tenderloin (or buy it pre-trimmed!). All excess fatty tissue on the outer surface of the meat should be removed, along with any connective tissue, prior to cooking. You can do this yourself with a sharp knife or get it ready to cook right from the butcher counter.
Check the temperature! A basic meat thermometer goes a long way when it comes to cooking the best pork. Check the temperature of your tenderloin regularly as it cooks and be sure to remove it as soon as it reaches between 140 and 145 degrees. The meat will continue cooking as it rests. Overcooking the pork even a little will greatly diminish the flavor and juiciness.
Let it rest. As great as this pork tenderloin smells when you pull it out of the oven and as tempting as it will be to dig your knife right in and gobble it up--don't. Letting the meat rest for about 10 minutes helps redistribute the juices, making it tender and even more flavorful. You can cover it with aluminum foil if you like to keep more of the heat in, but it's not necessary.