Remove the silver skin from the pork tenderloin. The silver skin is only on one side of the tenderloin. It's a small white/grey patch that runs about ½ of the way down the tenderloin.
Use a sharp knife to cut the silver skin off. You'll need to angle your knife down into the tenderloin and fully cut the patch away. It won't easily just pull off.
Mix the Dijon mustard and 1 tablespoon of extra virgin olive oil together in a small bowl. In a separate small bowl, combine the kosher salt, black pepper, garlic powder, fresh thyme, and fresh rosemary.
Add the potatoes and carrots to the hot skillet. Transfer the cast iron skillet to your preheated oven. Cook the Cast Iron Pork Tenderloin for 20 minutes at 400°F.
After 20 minutes, check the internal temperature of the pork using an instant-read thermometer. You should cook pork tenderloin to an internal temperature of at least 145°F.